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tei^% ^^.. 4.^'^^>-^&4v\. >''/i?^%"^.. .<4 



THE 

TINSMITH'S HELPER 



AND 



PATTERN BOOK 



WITH USEFUL RULES, DIAGRAMS AND 
TABLES 



BY H. K. VOSBURGH 



REVISED EDITION 



DAVID WILLIAMS COMPANY 

232-238 William St., New York City 
190T 






THt LIBRARY OP 

CONGRESS, 
Two Copies Received 

MAY. 13 1901 

COPYR40HT ENTRY 

CLASS^XXa I 
COPY 3. 



Copyright, 1879 
By H. K. VOSBURGH. 

Copyright, 1901 
By DAVID Wn,I,IAMS CO. 



/. 



J 



INTRODUCTORY. 

The first edition of this book appeared in 1879, ^^^ 
since then it has had a continual and increasing- sale. The 
author, H. K. Vosburgh, knew from experience the needs 
of the practical tinner and pi^epared a book in which a 
number of simple patterns were described in the plainest 
way. In preparing the new edition the cuts have been re- 
engraved and the appendix has been thoroughly revised, 
bringing the tables up to date and introducing new ones 
that have undergone changes since the first edition of the 
book appeared. 



INDEX 



ifAGE. 

Arc, To find the center of » .o. o ...... . 7 

Balls, To describe gores for pattern » , . , . , , 32 

Boiler block, Description of , , . 66 

Boiler, oval, To find length of sheet 26 

Breasts for cans, To describe 10 

Can breasts 11, 12 

Center of an arc. To find the 7 

Circle, To describe octagon within 9 

Cone, Old German rule for patterns 18 

Cone, Pattern for 13 

Cover, Oval boiler 27 

Elbow in five sections 58 

Elbow, To describe, quick method 53 

Flaring article, square top, rectangle base. To describe 

pattern 46 

Flaring article, top and base rectangles 48 

Flaring article with straight sides and round ends. To 

describe pattern 42 

Flaring hexagon article. To describe pattern 44 

Flaring oval vessel, two pieces, To describe pattern. . . 40 

Flaring square vessel. To describe pattern 45 

Flaring tinware. To describe patterns for 16 



Index. 5 

Flaring vessels in three pieces 20 

Flaring vessels. To describe pattern for 14 

Four-piece elbow, To describe 56 

Frustum of a cone 19, 21 

Funnel, Rectangular 22 

Gores for balls, To describe pattern for 32 

Heart with square and compass 30 

Hexagon article, flaring. To describe pattern 44 

Hood for stove pipes, To cut 15 

Measure lip 28 

Mensuration, Epitome of 69 

Obtuse elbow, To describe 60 

Octagon, tapering, To describe 47 

Octagon within circle, To describe 9 

Octagon within square. To describe 8 

Oval boiler cover 27 

Oval boiler. To find length of sheet 26 

Oval flaring vessel, four pieces, To describe patterns.. 43 

Oval, To describe 34, 36, ^"j 

Oval, To describe by string, pins and pencil 38 

Oval with diameters as 5 to 8, To describe 35 

Pitched cover 29 

Rectangular base and round top article 50 

Rectangular funnel 2.2 

Right angle elbow, To describe 52 

Round base and square top article 49 

Round top and rectangular base article 50 



6 Index. 

Round top and square base article. . . . » , o , . o 51 

Scale tray or scoop 24 

Scoop or scale tray 24 

Square base and round top article 51 

Square, To describe octagon within 8 

Square top and round base article 49 

Square vessel, flaring, To describe pattern 45 

Star, To describe a 31 

Steamer •. . . . 29 

Strainer pail 23 

Stringing patterns, Mode of 64 

String pattern 65 

Tables, rules and recipes 89 

Tapering elbow, To describe , 61 

Tapering octagon, To describe. 47 

Tea kettle body, To obtain length of piece .,, ... = .,. . 63 

Three-piece elbow, To describe ..„,.,.„ 54 

Watering pot breasts. ........ ,0,., 00 «... o ..... . 2}^ 



DIAGRAMS AND PATTERNS. 



To Find the Center of an Arc. 



Fig. I. 




Let H K represent the given arc. Span dividers any 
convenient radius and describe small arcs, as V O. Draw 
lines through them, as shown by dotted lines, and the in- 
tersection, S, wall be center sought. 



Rules and Diagrams. 



To Describe an Octagon Within a Given Square. 



Fig. 2. 




Draw diagonal lines from corner to corner and the in- 
tersection is the center H. With the compasses set to a 
radius from center to corner, and one foot set successively 
at each corner, describe the arcs, as shown. The points at 
which they cut the square, as K V, will be the corners of 
the octagon. Draw lines from point to point to complete 
the figure. 



Rules and Diagrams. 



To Describe an Octagon Within a Given Circle. 



Fig' 3' 



y^^ 




f \ 


/\ 


L K 1/- 


Hx\ y/y 


\^^ 


^^ 




.^P^ 



Draw lines at right angles passing through the center 
H. This divides the circle into four equal parts, which 
need only to be subdivided into equal parts again to form 
the corners for the octagon. This may be easily done by 
drawing the lines K V, bisecting, as shown, and drawing 
lines to the circle. 

The bottom will correspond in size to the size of the 
circle or square. Remember to allow for burr and double 
seam. 



lO 



Rules and Diagrams. 



To Describe Breasts for Cans. 



Fig. 4. 




Draw horizontal line H K, another parallel to it, V O, 
making the distance between the desired hight of breast. 
On H K lay off diameter of can, as S B. On V O, size of 
opening as U R, produce lines B R, S U, until they cross 
G. Span dividers from G to S, describe outer circle. G 
to U, describe inner circle. Set off outer circle equal to 
the diameter of the can B S Starting at B, draw line 
from G, allowing for locks, as shown by dotted lines. 
Reference can be made to the circumference table. 



Rules and Diagrams. 

Can Breasts. 

Pig- 5- 




Draw the two horizontal Hnes, K V and O S, and per- 
pendicular to them the line K H. Set off on line K V 
from the point B one-half the diameter of the can. On O 
S the point R is one-half the diameter of the opening. 
Produce the line U G, touching the points B and R, until 
it intersects H K. From U as center, with the radius U 
B, describe the outer circle. With the radius U R, the 
inner. Then span from K to B and step six times on large 
circle to obtain size of breast. Draw line to center and al- 
low for locks, as shown by dotted lines.- 



12 



Rules and Diagrams. 



Can Breasts. 

Fig. 6. 




Describe circle size of can. Draw line through center 
H. Span dividers three-fourths of diameter and strike 
circle K V. Span to diameter of can and step three times 
on large circle. 

Draw line from center to points K V, allowing for 
edges and locks. For more or less pitch make circle K 
V larger or smaller. 

Small circle in center for opening in top. Hoods and 
pitched covers may be cut by same rule. 



Rules and Diagrams. 



13 



Pattern for Cone. 



Fig. 7. 




H K V represents a cone for which an envelope is 
wanted. 

Span the dividers from V to H and describe the semi- 
circle O.S. Set off the circle equal in length to the cir- 
cumference of the required cone. Draw the lines V O 
and V S, allowing for locks or laps, as shown by the dot- 
ted lines. 

For the circumference, refer to the tables or obtain by 
some of the rules. By using the rules familiarity with 
them is obtained, which is desirable. 



14 



Rules and Diagrams. 



To Describe Pattern for Flaring Vessels. 



Fig. 8, 




For example, it is desired to describe pattern for pail 
12 inches in diameter at top, 9 inches at bottom and 9 
deep. 

Take the difference between large and small diameters 
(3 inches) for the first term, the hight for the second and 
the large diameter for the third, thus, 3:9 : : 12. 

12x9-^3, this gives radius by which the pattern may 
be described. Span the dividers (or use beam compasses, 
piece of wire, straight edge or any convenient device) 36 
inches and strike large circle. With radius less the hight 
of pail (9 inches) strike srnall circle, Ascertain the cir- 



Rules and Diagrams. 15 

cumference required and divide by the number of pieces 
to be used. Lay off on outer circle and draw lines to cen- 
ter, as H K V. 

Allow for locks, burr and wire. 



To Cut Hood for Stove Pipes. 

Span dividers size of pipe, describe circle, cut in to 
center, lap over and rivet. 

When sold by the pound there will be no waste. 



1 6 Rules and Diagrams. 

To Describe Patterns for Flaring Tinware 

Fig. p. 




By this figure and rule can be drawn any article of flar- 
ing tinware of any diameter, large or small. It is a rule 
of more extensive application than any other for getting 
correct patterns for frustums of a cone. It is the foun- 
dation for all curved work, cornice, bevels, chamfers, etc. 

H K V O represents the elevation of an ordinary tin 
pan, constructed in four pieces, 15^ inches in diameter at 
the top. Below the elevation is shown the same in plan ; 
the pan is a frustum of a cone, and if the sides of the pan 



Rules and Diagrams. 17 

were continued down until they intersected at S,as shown, 
the cone would be complete. The radius of the envelope 
of the cone must be either S H or S K. To describe the 
section of the frustum which is required, place one foot 
of the dividers at the center S, and with the radius S H de- 
scribe the arc K B. With the radius S V describe O U. 
This gives the width of pattern and the proper sweep. 

To get the length of the piece, refer to the table of 
circumferences or find, by the rules given, the circumfer- 
ence of the article, which in this case is 489/3 inches. There 
being four pieces, divide by four, which gives 12 5-32 
inches; span the dividers i inch, step off the 12 and add 
the fraction. 

Draw line from center S to point last ascertained. For 
locks, wire edge and burr allowance must be made. 



i8 



Rules and Diagrams. 



The Old German Kule for Patterns for the Cone. 



Fig. 10. 




Take the slant hight of the cone H K as a radius, and 
describe a circle. Divide the diameter of the base of the 
cone K V into seven equal parts and set off a space equal to 
twenty-two of these parts on the circle already struck. 
From the extremities thus measured off draw lines to the 
center. 

Allow for locks. 



Rules and Diagrams. 



19 



Frustum of a Cone. 



Fig. II. 




Lay the square on your sheet and construct the right 
angle H K V. Draw line O S parallel to K V, making the 
distance K O the altitude. On these lines lay off one-half 
the diameter of the large and small ends. Draw line 
through points V and S until they intersect at H ; then, 
with H as the center, describe the semicircles B U, R G. 
Lay off circumference of large end on line B U and draw 
lines to center H. Must allow for all edges. For two 
sections take one-half of the piece, allowing edges on 
piece used for pattern. 



20 



Rules and Diagrams. 



Flaring Vessel in Three Pieces. 



Fig. i^. 





< 


^^ 


— — 




V " 


, 





V'C^^^^^^' 


^^^^ 


\\ 




^V 




^\ 




\\ 


/, 


\\ 


// 


\\ 


// 


\\ 


// 


\\ 


// 


\\ 


// 


\\ 


// 


\\ 


// 


V 


4/ 



Draw line H K; perpendicular to it, lines parallel to 
each other apart the hight of vessel. With the intersec- 
tions, as V, O for centers, describe circles size of top and 
bottom of vessel. Draw lines S H and B H touching on 
circles, and at intersection H as center, with the radius H 
V, describe the segment U R; with the radius H O, the 
segment G F. Allow for locks, as shown by dottted lines. 



Rules atid Diagrams. 



21 



Frustum of a Cone. 



Fig- 13- 




Draw perpendicular line H K, and from K lay off 
diameter of large end, as V O on the line H K the hight 
of frnsturn, as K S. Draw line parallel to V O, and on it 
lay off small diameter, as B U. Draw lines through points 
V B and O U until they intersect at H. Span compasses 
from H to V and draw large arc R G ; from H to B and 
describe small arc. Allow for all edges, wire, burr and 
locks. This forms a pattern in one pice. 



Rules and Diagrams. 

Rectangular Funnel. 

Fig. 14. 



K O 




Draw side elevation, as H K V. Continue side lines as 
shown by dots. From point of intersection as center, de- 
scribe arc and chord K V and H. Draw end elevation O 
K S, lines produced to intersect at B. From B as center 
describe arc and chord O K and S. The other side and 
end obtained in the same manner, as shown in cut. Can 
be made in two or more pieces by dividing. All locks and 
edges must be allowed for on the pattern piece. 



Rules and Diagrams. 



For Strainer Pail or Watering Pot Breast. 



Fig. 15- 




Strike circle size of pail or pot. Span dividers i}i 
inches, more or less, being governed by pitch desired, as 
from V to K, and describe the arc. Draw the chord, mak- 
ing the segment which is the pattern the desired width. 
The breast may be cut out if preferred, as shown by dot- 
ted lines. 



24 



Rules and Diagrams. 



Scale Tray or Scoop. 

Fig. 16. 




Construct a sectional view of the scoop, as H K V ; it 
being made in two pieces, let H S B represent one-half 
elevation of it. Continue the lines B S and H K until they 
cross at U. Divide H K V into any given number of 
spaces, continuing the same to the line H B, as shown by 
short lines. Then from the point U to the division points 
on the line H B, with rule crossing the line S H, mark 



Rules and Diagrams. 25 

the intersections on the line S H. With the T square at 
right angles with H U, drop the points thus obtained on 
H S onto the line B S. 

With U as center and U B as a radius describe the 
arc B R. Step off upon it spaces equal to the length H K 
V, with dividers set the same, which gives the length B R. 
Draw radial lines from U to space marks on line B R, as 
shown. 

Span the dividers from U to G on the line U B and 
carry the distance to the first radial line; do likewise with 
all those spaces on the line. Then a line traced through 
the points thus obtained, together with the arc B R, will be 
the outline of the required pattern. Allow for edges, as 
shown by dotted lines. 



26 



Rules and Diagrams. 



To Find Length of Sheet Required for Oval Boiler. 
Common Method. 

Fig. ly. 





Describe bottom, length and width desired, and from 
H as a starting point roll on the bench to obtain circum- 
ference. If three pieces are to be used, cut the circum- 
ference of the bottom, edges being allowed ; if but two, }i 
inch smaller; if but one, ^^4 inch smaller; if more than 
three pieces, add ^, inch for every extra piece; or, to 
twice the length of the bottom add the width and allow 
y?. inch for every lock or seam. Cut the cover the same 
size as bottom, by figure. 

Or, burr, bottom and roll as above. Use strip i}4 
inches less in length after locks are all turned. 



Rules and Diagrams. 



27 



Oval Boiler Cover 



Fig. 18. 




Draw line R K, and from R as center describe circle 
G U, size of the boiler outside of rod. On the line R K 
erect line H V. From center R to S, one-half entire length 
of boiler ; from S to K, fi inch or more if more pitch is de- 
sired. Lay corner of square on line at H, one blade at K, 
the other touching circle, describe lines U H K ; corner at 
V, G V K. Allow for locks and notch for edges. 



28 



Rules and Diagrams. 



Measure Lip. 

Fig. ig. 




Draw line H K and upon it, with V as center, describe 
circle size of measure. With S as center, half distance 
from V to H, describe semicircle B U. With V as cen- 
ter describe G O the desired width. Cut on B U and G 
O to obtain the lip. 



Rules and Diagrams. 



29 



Steamer or Pitched Cover. 



Fig. 20. 




Strike circle one inch larger than rim burred. Draw 
line through center H, and from either side i inch on cir- 
cle to I inch from center K. Draw lines and cut out. Or. 
strike circle the same or larger. Draw line through cen- 
ter and cut on it to center. After burring put in rim; 
draw up and mark, cutting out triangular piece and sol- 
dering. Much quicker and equally as good. 



30 



Rules and Diagrams. 



Heart with Square and Compass. 



Fig, 21. 




Draw line H K and on it two semicircles. Span di- 
viders from H to K and make sweep to V. Let H to K 
represent the breadth of the heart. 



Rules and Diagrams. 



3i 



To Describe a Star. 

Fig. 22. 




From V as center strike circle size of star desired. 
Open dividers to one-fifth of circumference, make five 
steps on circle and draw lines to points. 

There is a rule for finding the points of a star other 
than stepping, but I do not give it. I have found the 
mode given to be the quickest and most accurate. 



i2 



Rules and Diagrams. 



Pattern for Cutting Balls. — To Describe the Gores. 



Fig. 23, 




Erect perpendicular line H K equal to one-half the 
circumference of the ball ; divide this line into one-half 
as many equal parts required ; make the line V O equal 
to one of these pieces, cutting H K through the center 
at right angles ; then with H and K as centers, with radius 
greater than one-half the distance K S, describe the two 
^rcs B U ; with V and as centers, arcs R G ; draw lines 



Rules and Diagrams. 33 

through these points, as shown by clotted Hnes. From 
points of intersection describe arcs H V K and H O K, 
and you obtain pattern for one piece. Allow for laps or 
seams. The more pieces used the better globe produced. 
Good results obtained by slightly raising the pieces. 



34 



Rides and Diagrams. 



To Describe an Oval. 



Fig. 24. 




Draw horizontal line F K, span the dividers one-third 
the required major diameter, and from V and O as centers 
describe circles, as shown ; then span dividers two-thirds 
entire length, and, with one foot at the intersection of the 
circles, as S and B, draw the arcs G H and U R, which 
completes the oval. 

The proportion of the diameters is about as 3 to 4. 



Rules and Diagrams. 



35 



To Describe Oval with Diameters as 5 to 8. 



Fig. 25. 




Draw horizontal line H K. Span compasses one- 
quarter the long diameter and describe three circles with 
that radius, as shown by diagram. Then draw lines 
through centers of outer circles and their intersections, 
as shown. The oval is completed by drawing the arcs con- 
necting the outer circles from points V and O as centers. 



36 Rules and Diagrams. 

To Describe an Oval. Another Method. 

Fig. 26. 




Draw horizontal line H K and perpendicular to it V O. 
Let H K equal the long or transverse diameter, and' S B 
the short or conjugate. Lay off the distance S B on the 
line H K, as from H to U. Divide the distance U K into 
three equal parts. From R, the center, set off two of the 
parts each side, as G F. On the line V O set off the dis- 
tance G F from R, as R V and R O. From V and O 
draw lines passing through G and F, as shown. From 
the points V, O, G, F as centers describe the arcs that 
complete the ellipse. 



Rules and Diagrams. 37 

To Describe an Oval. Another Method 

Fig. 2^. 




Construct the parallelogram equal in length and width 
to the long. and short diameters of the oval desired. Di- 
vide it into four equal parts by drawing lines through the 
center, crossing at H. Mark the points K and K one-third 
the distance from V to H, and draw lines from the corners 
through these points until they intersect, as shown at O. 
Then from O and O as centers describe the arcs SUB 
and SUB; from K and K as centers the segments B V B 
and S V S. 



38 



Rules and Diagrams. 



To Describe Oval by Means of String, Pins and 

Pencil. 

Fig. 28. 



/ \ 



/_ 


^ X 


^_ 


-A 



Erect perpendicular line H K equal to short diarneter 
and at right angles to it \' O. Span dividers one-half the 
length of the oval, and with H and K as centers describe 
the arcs S and B. Set pins at these points, and, with a 
string (one that will not stretch) tied around them so 
that the loop when drawn tight will reach H or K, as 
shown, draw the figure with pencil, keeping string equally 
tense whyle going around. Of all the apparatus invented 



Rules and Diagrams. 39 

for oval drawing I think the string is the best. The best 
results, at least, are obtained. To attempt to draw a per- 
fect oval or ellipse by the use of compasses is vain. It 
cannot be done so that the line will be true, or the propor- 
tion or shape satisfactory to one with an eye for correct- 
ness or uniformity. The so-called trammels are the next 
best thing, but no better. A few rules for drawing ovals 
by the use of dividers have been given in this work so 
the mechanic may take his choice, and after a little prac- 
tice with the string and nails will find them the best tram- 
mels vet invented for the purpose. 



40 



Rules and Dia (grains. 



To Describe Pattern for Flaring Oval Vessel. 
Two Pieces. 

Fig, 2p, 




Construct right angle H K V and parallel to H K, O 
G, the distance between hight of article. Lay off on H K 
and O G one-half the circumference of the arc SUB, 
Fig. 2y, for top and bottom of vessel. Draw line through 
these points to intersect with line K V. With V as center 
and radius V H describe arc H B ; with radius less the 



Rules and Diagrams. 4i 

higlit, as V O, describe arc O U. Set off the distance 
H K to B and draw line from this point to center. Lay 
off the horizontal lines one-half the circumference of the 
arc S V S, Fig. 27, for top and bottom, as R K, G S. Draw 
lines through these points to intersect with perpendicular 
line at A. Take raduis A G on the lines K V and H V, 
as D O and C U, and describe the arcs O E and U F ; also, 
from same center, the top arcs. Set off on the arcs U F 
and O E the distance V S, Fig. 27. Draw lines through 
these points to centers C and D. Allow for all edges, 
locks, wire and burr. 



42 



Rules and Diagrams. 



To Describe Pattern for Flaring Article with Straight 
Sides and Round Ends. Two Pieces. 




Erect two perpendicular lines, H V, K O, distance be- 
tween the length of sides ; at right angles to these, two 
lines, distance between the slant hight of article. Set oft* 
from lines H V and K O one-half the circumference of 
the ends, top and bottom, and produce lines through these 
points until they intersect at V and O. From V and O as 
centers, with radii V B and V H, describe arcs, as S R, 
B U, which complete the pattern. Allow for all edges, 
locks, wire and burr. 



Rules and Diagrams. 



43 



To Describe Pattern for Oval Flaring Vessel. 
Four Pieces. 

Pig' 3I' 




Describe bottom as by Figs. 27 or 28. Obtain length 
of arcs SUB and S V S, also length of corresponding 
arcs at the top and bottom of vessel. Draw horizontal 
lines H K and V O, making the distance between the de- 
sired hight. Make H K equal in length to that of the 
piece at the top, and V O to that of the bottom, for the 
sides. S B and U R for the end pieces. Produce lines 
through these points to intersect at G and G'. Describe 
the arcs from these points. Allow for all edges, locks, 
wire and burr. 



44 Rules and Diagrams. 

To Describe Pattern for Flaring Hexagon Article. 

Fig' 3^' 




Draw side elevation, as V O R G, producing side lines 
until they cross in the center, as shown by dotted lines. 
Span dividers from center to O, and describe circle H O 
U ; span to G and describe inner circle ; span again from V 
to O and step on the outer circle three spaces each side 
from O, as V, K, H, S, B, U. Draw lines from these 
points tending toward center, and connect by chords, as 
H K, K B, etc. Cut out piece H U, allowing for locks, as 
shown. Pattern for a pentagon article may be described 
by the same rule. 



Rules and Diagrams. 



45 



Describe Pattern for Flaring Square Vessel, 



Fig. 33- 




Draw side elevation, as K V, B U, side lines continued 
until they intersect at R. Make K B the slant hight. 
With radius R K, strike circle U B G. Span dividers from 
K to V and set off on outer circle the distance, as V O, 
H S, etc. ; draw lines through these points tending toward 
the center R, also the chords, as shown by dotted lines. 
Allow for edges. Can be made in two pieces by dividing 
and allowing for extra lock or seam. 



46 



Rules and Diagrams. 



To Describe Pattern for Flaring Article with Square 
Top and Base a Rectangle. Two Pieces* 

Pig- 34- 




Draw horizontal lines H K and V O, making the dis- 
tance between the slant hight. Set off on H K the length 
of the longest side, and on V O the length of one side of 
the top. Draw lines through these points, as H V, K O. 
With a radius equal to one-half of the difference between 
the shortest side of the base and one side of the top, de- 
scribes the arcs S and B. With the blade of the square 
resting on the arc and the corner at H, draw the right 
angle U H S ; the other side the same. Set off the lines 
U H and K V, equal in length to one-half the short sides, 
and draw lines at right angles to U H and K V ; also lines 
G Y, G O at right angles to U G and R G. Allow for 
locks and edges, , , 



\ > 



Rules and Diagrams. 



47 



To Describe Tapering Octagon. 



Fig' 35- 




Draw plan of one side, as H K V, and continue side 
lines until they intersect at O. With O as a center and the 
radii O V and O H, describe inner and outer circles. Set 
off on them distances equal to sides of base and top, and 
connect by chords, as shown by dotted lines. Allow for 
^ocks and edges. 



43 



Rules and Diagrams. 



Flaring Article, Top and Base a l^ectangle. Two 

Pieces. 



Fig. ^6. 




Draw side elevation, as H K, V O, of the longest side. 
Span dividers the difference between the shortest side of 
the base and longest side of top. From V and O as cen- 
ters describe arcs S and S. With blade of square resting 
on arcs and the corner at H and K, draw lines H B and 
K G. Set off H B and K G equal one-half of shortest 
sides of base ana draw lines B U and G R at right angles 
to H B and K G ; also lines U V and R O at right angles 
to U B and G R. Allow for locks, as shown by dotted 
lines. 



Rules and Diagrams. 



49 



Round Base and Square Top Article. Two Pieces. 



Pig- 37- 




Erect perpendicular line. Span dividers to three- 
quarters diameter of base and describe semicircle H K V. 
Set off equal to one-half the diameter of base H K and 
draw lines to center. Span dividers to one-half size of 
top, from corner to corner, and describe inner circle. Lay 
out sides of top, size required, on circle, as shown. Allow 
for locks. 



50 



Rules and Diagrams. 



Rectangular Base and Round Top Article. 



Fig- 3S. 




Draw horizontal lines H K, V O. Make H K equal 
to the longest side of base, V O equal to one-fourth the 
circumference of the top, the distance between slant 
hight; draw side lines through these points, which gjves 
side elevation. With radii one-half the difference between 
V O and the shortest side of the base, describe the arcs 
S, B ; with blade of square resting on arcs, and corner at 
H and K, draw lines K R, H U; at right angles to K R, 
H U, draw lines R G and U G ; U G and R G produced 
to intersect ; from this point span dividers to line V O and 
describe the arc. Allow for locks and edges. 



Rules and Diagrams. 



51 



Square Base and Round Top Article. Two Pieces. 



Fig. 39- 




Draw horizontal lines H K, V O ; H K equal to the 
length of one side of the base, V O equal to one-fourth 
the circumference of the top, tHe distance between the 
slant hight ; draw lines through these points, which gives 
side elevation ; with radii one-balf the difference of the two 
ends, describe arcs ; with blade of square resting on arcs 
and the corner at H and K, draw lines H S and K B ; at 
right angles to H S and K B, S U and B R, produced to 
intersect at G. Span dividers from G to line V O and 
describe the arc. Allow for locks and edges. 



52 Rules and Diagrams. 

To Describe a Square or Right Angle Elbow. 
Two Pieces. 

Fig. 40. 




Draw the elevation of the elbow, as B S, O V, K H. 
Draw line from V to O. Divide one-half of the plan 
into a convenient number of equal parts, as shown by 
dotted lines ; draw lines at right angles to these, starting, 
as shown, at the miter line. Make the line R U equal 
in length to the circumference of the elbow, and draw, 
directly opposite, the outer end of the elbow. Set off on 
this line spaces corresponding to those in the plan, the 
same number each side of the center line ; then draw lines 
parallel to the other arm of the elbow, cutting the corre- 
sponding lines as indicated. By tracing through these 
points the irregular line U G the pattern is obtained. Al- 
low for locks or rivets. 

The general principle for cutting elbow patterns is the 
same throughout, and to understand the principle is to be 
able to describe pattern for any elbow, at any angle and of 
any number of pieces. It is the design of this work to 
make the principle clear. 



Rules and Diagrams. 



53 



Quick Method. 



Fig. 41. 




Lay out on sheet length and width required for elbow, 
as H K, O \" ; divide into four equal parts, as shown. 
Span dividers size of pipe and from S as center describe 
the arc B. From U and G, with one-half radius, describe 
the arcs A, R. Draw lines to connect, as shown. A very 
quick way to get a pattern, but will need some trimming. 
Allow for locks. 



54 



Rules and Diagrams. 



To Describe Three-Piece Elbow. 



Fig. 42. 




Lay out two curved lines, H K and V O, corresponding 
to the desired length of the elbow, making the distance be- 
tween the diameter. Lay off the circles into three divisions 
by drawing the lines S B and S U. Describe O K and 
divide into any convenient number of parts, as shown 
by figure. 



Rules and Dia grams. 



55 



Fig' 43' 



H 
















I 


3 
















V 










if 


















































































































1 


1 


























• 


























( 


a 






























R 


K 
















< 


5 


_ 


















Construct the parallelogram H V K O, equal in length 
to the circumference of the elbow. Draw through the 
center the perpendicular line S B, and set ofif each side of 
the sam6 spaces corresponding to those in the semicircle 
O K, making each line of the same length, as K U, O R, 
etc. A line traced through these points will give pattern 
for that piece. To obtain pattern for middle piece, it will 
be necessary to get the length of the lines only ; set off each 
side of B S as before and trace line through the points; 
so also the third piece. Allow for locks or rivets. 



56 



Rules and Diagrams. 



To Describe a Right Angle Elbow. Four Pieces. 



Pig- 44- 




Describe the two curved lines H K and V O corre- 
sponding to the desired length of the elbow, making the 
distance between the diameter of the pipe. Make four 
divisions by the lines S B, S U, S R. Describe the semi- 
circle and divide into any convenient number of spaces, as 
shown by the figure. 



Rules and Diagrams. 



57 



Pig' 45- 



Construct the parallelogram H V K O, equal in length 
to the circumference of the elbow. Draw through the 
center the perpendicular line S B, and set ofif each side of 
it lines corresponding in length to those in the semicircle 
O K, as described on page 55. To obtain pattern fof the 
other pieces, proceed as there described. Allow for locks. 



5» 



Rules and Diagrams. 



Elbow in Five Sections. 



Fig. 46. 







\ \ 


/■~^\ 


/ V- 




/ Yz 




r: 


i"^-- 


J— 




/ 


/"^^^ 


\ ^ ^ — 






To obtain pattern for elbows of any angle and any 
number of pieces, it is only necessary to draw a plan of the 
elbow corresponding in size, number of sections and the 
desired angle, divide it into any convenient number of 
equal spaces and proceed as shown on the following page. 



Rules and Diagrams, 



59 



Fig' 47- 



Construct the parallelogram and draw lines each side 
of center corresponding to the number of equal parts the 
semicircle is divided into, and then set ofif on each of these 
lines the .length of the same line in the plan and trace 
through these points to obtain the desired pattern. Every 
piece must be obtained in the same manner or trimming 
will be necessary. Reversing pieces to obtain pattern for 
the next is not altogether reliable, yet perhaps near 
enough for practical purposes, as trimming is generally 
done. 



6o Rules and Diagrams. 

To Describe Pattern for Obtuse Elbow. 



Fig. 48. 




mm 



It is probably more desirable to fully understand the 
principle of obtaining elbow patterns at obtuse angles than 
any other, and when it is understood one can cut pattern 
for any elbow without difficulty. The principle is the 
same as has been explained, and, after having drawn a 
correct representation of elbow, proceed as by rules 
already given and the result will be satisfactory. T's of 
all sizes and angles are described in the same manner. 
First draw an elevation of the desired T, and on the pipe 
at the desired angle, and it will be plain. 



Rules and Diagrams. 



61 



To Describe a Tapering Elbow. 

Fig. 49. 




62 Rules and Diagrams. 

Draw plan of elbow with both ends. Strike first and 
at any angle desired, drawing miter line, as shown. Then, 
each side of the center, lay ofif one-half diameter of small 
end and produce lines through these points to intersect. 
With radius from center to ends of elbow, describe the arcs 
and divide into a number of equal parts and make each 
correspond with the lines in the plan ; a line traced through 
these points will give the pattern. Allow for locks. 

All miter joints obtained in the same manner, whether 
for elbows, gutters or cornices. 



Rules and Diagrams. 



63 



To Obtain Length of Piece for Tea Kettle Body. 



Fig. 50^ 




V 



The way in general practice is to roll the bottom after 
burring on the bench to obtain circumference, and use 
strip ^ inch less in length, as shown by figure. H repre- 
sents the pit ; K V the length of the strip or sheet. Or, 
make the body Y^ inch less in diameter than the pit or 
breast, for double seam; for snap or spring bottoms, 
Va inch. 



64 



Rules and Diagrams. 



Mode of Stringing Patterns. 



Fig- 5I' 




This cut represents the three pieces of a 6-quart pan 
usually cut from one sheet of 10 x 14 tin. Instead of using 
one piece for pattern and placing it three times, three 
pieces are fastened together by soldering on two strips of 
tin with a heavy hem on each side, and all placed at once, 
thus saving time and vexation. To use to advantage 
begin at the bottom of the string pattern and mark around 
on the outside first, and then mark in the centers. 



Rules aiid Diagrams. 



65 



String Pattern. 

Fig' 5^' 



e 



This figure represents a string of rim or hoop pat- 
terns, fastened as shown in the same manner as described 
on page 64. Rims of any width can be put together in 
this manner and a great saving of time is the result when 
once properly done. Patterns for all articles of tinware 
should be strung in this way, when more than one piece 
is obtained from a sheet, that the marking out may be ex- 
pedited and less tedious. 



66 



Rules and Diagrams. 



Description of Boiler Block. 



Pig' 53- 



By this figure is represented a block for truing up 
boilers after they are formed up in the rollers and locked 
together. Many mechanics depend upon the stake and 
the accuracy of the eye, but after using this method would 
not abandon it, as better results are obtained and in much 
less time. The block is made of 2-inch plank, by placing 
one on another and securing with four long bolts passing 
through them. The proper dimensions are as follows: 

Bottom, 13 inches wide, 25 inches long. 

Top, 10 '' '' 19 " 

Hight, 12 " 



APPENDIX. 



EPITOME OF MENSURATION. 



OF THE CIRCLE, CYLINDER, SPHERE, ETC. 

1. The circle contains a greater area than any other 
plane figure bounded by an equal perimeter or outline. 

2. The areas of circles are to each other as the squares 
of their diameters. 

3. The diameter of a circle being i, its circumference 
equals 3.1416. 

4. The diameter of a circle is equal to .31831 of its 
circumference. 

5. The square of the diameter of a circle being i, its 
area equals .7854. 

6. The square root of the area of a circle multiplied 
by 1. 12837 equals its diameter. 

7. The diameter of a circle multiplied by .8862, or the 
circumference multiplied by .2821, equals the side of a 
square of equal area. 

8. The number of degrees contained in the arc of a 
circle multiplied by the diameter of the circle and by 
.008727, the product equals the length of the arc in equal 
terms of unity. 

9. The length of the arc of a sector of a circle multi- 
plied by its radius equals twice the area of the sector. 

10. The area of the segment of a circle equals the area 
of the sector, minus the area of a triangle whose vertex 



70 Epitome of Mensuration. 

is the center and whose base equals the chord of the seg- 
ment. 

1 1. The sum of the diameters of two concentric circles 
multiplied by their difference and by .7854 equals the area 
of the ring or space contained between them. 

12. The circumference of a cylinder multiplied by its 
length or hight equals its convex surface. 

13. The area of the end of a clyinder multiplied by its 
length equals its solid contents. 

14. The area of the internal diameter of a cylinder 
multiplied by its depth equals its cubical capacity. 

15. The square of the diameter of a cylinder multiplied 
by its length and divided by any other required length, 
the square root of the quotient equals the diameter of the 
other cylinder of equal contents or capacity. 

16. The square of the diameter of a sphere multiplied 
by 3.1416 equals its convex surface. 

17. The cube of the diameter of a sphere multiplied 
by .5236 equals its solid contents. 

18. The hight of any spherical segment or zone, multi- 
plied by the diameter of the sphere of which it is a part 
and by 3.1416, equals the area or convex surface of the 
segment ; or, ' 

19. The hight of the segment multiplied by the cir- 
cumference of the sphere of which it is a part equals the 
area. 

20. The solidity of any spherical segment is equal to 
three times the square of the radius of its base, plus the 
square of its hight, multiplied by its hight and by .5236. 

21. The solidity of a spherical zone equals the sum 
of the squares of the radii of its two ends and one-third 



Epitome of Mensuration. >j i 

the square of its bight, multipHed by the bight and by 
1.5708. 

22. The capacity of a cybnder, i foot in diameter and 
I foot in length, equals 5.875 United States gallons. 

23. The capacity of a cylinder, i inch in diameter and 
I foot in length, equals .0408 United States gallon. 

24. The capacity of a cylinder, i inch in diameter and 
I inch in length, equals .0034 United States gallon. 

25. The capacity of a sphere i foot in diameter equals 
3.9168 United States gallons. 

26. The capacity of a sphere i inch in diameter equals 
.002266 United States gallon ; hence, 

2y. The capacity of any other cylinder in United States 
gallons is obtained by multiplying the square of its diame- 
ter by its length, or the capacity of any other sphere by the 
cube of its diameter and by the number of United States 
gallons contained as above in the unity of its measurement. 

OF THE SQUARE, RECTANGLE, CUBE, ETC. 

1. The side of a square equals the square root of its 
area. 

2. The area of a square equals the square of one of its 
sides. 

3. The diagonal of a square equals the square root of 
twice the square of its side. 

4. The side of a square is equal to the square root of 
half the square of its diagonal. 

5. The side of a square equal to the diagonal of a given 
square contains double the area of the given square. 

6. The area of a recangle equals its length multiplied 
by its breadth. 



72 Epitome of Mensuration. 

7. The length of a recangle equals the area divided by 
the breadth ; or the breadth equals the area divided by the 
length. 

8. The solidity of a cube equals the area of one of its 
sides multiplied by the length or breadth of one of its 
sides. 

9. The length of a side of a cube equals the cube root 
of its solidity. 

10. The capacity of a 12-inch tube equals 7.48 United 
States gallons. 

OF TRIANGLES, POLYGONS, ETC. 

1. The complement of an angle is its defect from a 
right angle. 

2. The supplement of an angle is its defect from two 
right angles. 

3. The three angles of every triangle are equal to two 
right angles : hence the oblique angles of a right angled 
triangle are each other's complements. 

4. The sum of the squares of two given sides of a 
right angled triangle is equal to the square of the hypothe- 
nuse. 

5. The difference between the squares of the hypothe- 
nuse and given side of a right angled triangle is equal to 
the square of the required side. 

6. The area of a triangle equals half the product of the 
base multiplied by the perpendicular bight. 

7. The side of any regular polygon multiplied by its 
apothem or perpendicular, and by the number of its sides, 
equals twice the area. 



Epitome of Mensuration. 73 

OF ELLIPSES, CONES, FRUSTUMS, ETC 

1. The square root of half the sum of the squares of 
the two diameters of an elhpse multiplied by 3.1416 equals 
its circumference. 

2. The product of the two axes of an ellipse multiplied 
by .7854 equals its area. 

3. The curve surface of a cone is equal to half the 
product of the circumference of its base multiplied by its 
slant side, to which, if the area of the base be added, the 
sum is the whole surface. 

4. The solidity of a cone equals one-third the product 
of its base multiplied by its altitude or hight. 

5. The square of the diameters of the two ends of the 
frustum of a cone added to the product of the two diame- 
ters, and that sum multiplied by its hight and by .2618, 
equals its solidity. 



DEFINITIONS OF ARITHMETICAL SIGNS USED 
IN THE FOLLOWING CALCULATIONS. 



= Sign of Equality, and signifies as j + 6 = lo. 



+ 


" Addition, 


i i. 


as 6 + 6 = 12, the Sum 


— 


" Subtraction, 


a 


as 6 — 2 = 4, Remain- 
der. 


X 


" Multiplication, 


(( 


as 8 X 3 = 24, Product. 


-j- 


' Division, 


i b 


as 24 H- 3 = 8, 


V 


" Square Root, 


i i 


Extraction of Square 
Root. 


6' 


' to be squared, 


ii. 


thus 8^ = 64. 


r 


*' to be cubed, 


i i 


thus 33 = 27. 



DECIMAL EQUIVALENTS TO FRACTIONAL 
PARTS OF LINEAL MEASUREMENT. 



ONE INCH THE INTEGER OR WHOLE NUMBER. 



.96875 


equal 


% and 3-32 


.46875 


equal 


% and 3-32 


.9375 


" 


% and 1-16 


.4375 


" 


% and 1-16 


.90625 


" 


% and 1-32 


.40625 


" 


% and 1-32 


.S75 


" 


Ys 


.375 


" 


% 


.84375 


«' 


% and 3-32 


.34375 


•' 


1/4 and 3-32 


.8125 


" 


% and 1-16 


.3125 


" 


1/4 and 1-16 


.78125 


" 


% and 1-32 


.28125 


" 


14 and 1-32 


.75 


" 


% 


.25 


" 


% 


.71875 


" 


% and 3-32 


.21875 


" 


Vs and 3-32 


.6875 


" 


% and 1-16 


.1875 


" 


Vs and 1-16 


.65625 


" 


% and 1-32 


.15625 


" 


Vs and 1-32 


.625 


" 


% 


.125 


" 


Vs 


.59375 


'♦ 


i/o and 3-32 


.00375 


" 


3-32 


.5625 


" 


i/o and 1-16 


.0625 


" 


1-16 


.53125 


" 


1/2 and 1-32 


.03125 


" 


1-32 


.5 


" 


1/2 









ONE FOOT OR TWELVE INCHES THE INTEGER. 



9166 


' equal 


11 inches. 


.1666 - 


8333 


" 


10 


' 


.0833 


75 


" 


9 


' 


.07291 


6666 




8 


♦ 


.0625 


5833 


" 


7 


' 


.05208 


.5 


" 


6 


• 


.04166 


.4166 


" 


5 


• 


.03125 


.3333 


" 


4 


• 


.02083 


.25 


«♦ 


3 


' 


.01041 



equal 



2 inches 
1 

% 
% 
% 



MENSURATION OF SURFACES. 



Mensuration is that branch of Mathematics which is 
employed in ascertaining the extension, soHdities and ca- 
pacities of bodies capable of being measured. 



MENSURATION OF SURFACES. 

To Measure or Ascertain the Quantity of Surface In Any 

Right Lined Figure i^^hose Sides are 

Parallel to £ach Other. 

Rule. — Multiply the length by the breadth or perpen- 
dicular hight, and the product will be the area or superfi- 
cial contents. 

Application of the Rule to Practical Purposes. 

The sides of a square piece of iron are g}i inches in 
length, required the area. 

Decimal equivalent to the fraction % ^ .875, and 9.875 
X 9.875 = 97-5, etc., square inches, the area. 

The length of a roof is 60 feet 4 inches and its width 
25 feet 3 inches ; required the area of the roof. 

4 inches = .333 and 3 inches = .25 (see table of equiv- 
alents), hence, 60.333 X 25.25 = 1523.4 square feet, the 
area. 



Epitome of Mensuration. 77 

TRIANGLES. 

To Fiud the Area of a Triaii<fle Wbea the Base and Per- 
pendicular are Given. 

Rule. — Multiply the base by the perpendicular hight 
and half the product is the area. 

The base of the triangle is 3 feet 6 inches in length 
and the hight i foot 9 inches ; required the area. 

6 in. = .5 and 9 in. = .75, hence, ^'^ ^ ^'^^ = 3-0625 

2 
square feet, the area. 

Any Two Sides of a Right Angled Triangle being Given, to 
Find the Third. 

When the Base and Perpendicular are Given to 
Find the Hypothenuse. 

Add the square of the base to the square of the perpen- 
dicular and the square root of the sum will be the hypothe- 
nuse. 

The base of the triangle is 4 feet and the perpendicular 

3 feet ; then 4- -f 3^ = 25, V25 = 5 feet, the hypothenuse. 

When the Hypothenuse and Base are Given to Find 
THE Perpendicular. 

From the square of the hypothenuse subtract the 
square of the base, and the square root of the remainder 
will be the perpendicular. 

The hypothenuse of the triangle is 5 feet and the base 

4 feet ; then 5- — 4" = 9, and V9 == 3, the perpendiculafc 



jS Epitome of Mensuration. 

When the Hypothenuse and Perpendicular are 
Given to Find the Base. 

From the square of the hypothenuse subtract the 
square of the perpendicular, and the square root of the re- 
mainder will be the base. 



OF POLYGONS. 

To Find the Area of a Regular Polygon. 

Rule. — Multiply the length of a side by half the dis- 
tance from the side to the center, and that product by the 
number of sides; the last product will be the area of the 
■figure. 

Example. — The side of a regular hexagon in 12 
inches, and the distance therefrom to the center of the 
figure is 10 inches ; required the area of the hexagon. 

X 12 X 6 =360 square inches = 2^ square feet. Ans. 

2 

To Find tlie Area of a Regular Polygon ivben the Side Only 

is Given. 

Rule. — Multiply the square of the side by the multi- 
plier opposite to the name of the polygon in the ninth 
column of the follozving table, and the product zvill be the 
area. 

Table of angles relative to the construction of Regular 
Polygons with the aid of the sector, and of coefficients to 
facilitate their construction without it ; also, of coefficients 



Epitome of Mensuration. 79 

to aid in finding the area of the figure, the side only being 
given. 

.^2 0-2 .g V^ l'-^^'^<'^--X. 1 = 

as wg "So-i &-S flS'S -dS ^ -d S a' S'S 

3a3 flo £3^^ 0)^3 S^i-^WM—csCl.-- fcH-Q 

Names. '7'^ < < P^h-JKi:^ ■< 

T'riangle 3 120 60 .2SS68 1.782 .5773 2. .433012 

Square 4 90 90 .5 1.414 .7071 1.414 1. 

I'entagon 5 72 108 .6S82 1.175 .8506 1.238 1.720477 

Hexagon 6 60 120 -.866 1. 1. l.i:6 2.598076 

Heptagon 7 51 3-7 128 4-7 1.0382 .8672 1.152 1.11 3.633912 

Octagon 8 45 135 1.2071 .7654 1.3065 1.08 4.828427 

Nonagon 9 40 140 . 1.3737 .684 1.4619 1.06 6.181824 

Decagon 10 36 144 1.53S8 .618 1.618 105 7.694208 

Undecagon 11 32 8-11 147 3-11 1.7028 .5634 1.7747 1.04 9.36564 

Dodecagon 12 30 150 1.866 .5176 1.9318 1.037 11.196152 

Note. — " Angle at center " means the angle of radii 
passing from the center to the circumference or corners 
of the figure. " Angle at circumference " means the 
angle which any two adjoining sides make with each 
other. 



THE CIRCLE AND ITS SECTIONS. 



Observations and Definitions. 



1. The circle contains a greater area than any other 
plane figure bounded by the same perimeter or outline. 

2. The areas of circles are to each other as the squares 
of their diameters ; any circle twice the diameter of an- 
other contains four times the area of the other. 

3. The radius of a circle is a straight line drawn from 
the center to the circumference. 

4. The diameter of a circle is a straight line drawn 



8o Epitome of Mensuration. 

through the center and terminating both ways in the cir- 
cumference. 

5. A chord is a straight Une joining any two points of 
the circumference. 

6. The versed sine is a straight hne joining the chord 
and the circumference. 

7. An arc is any part of the circumference. 

8. A semicircle is half the circle cut ofif by a diameter, j 

9. A segment is any portion of a circle cut off by a 
chord. 

10. A sector is a part of a circle cut off by two radii. 



General Rules in Relation to the Circle. 

1. Multiply the diameter by 3.1416, the product is the 
circumference. 

2. Multiply the circumference by .31831, the product is 
the diameter. 

3. Multiply the square of the diameter by .7854 and the 
product is the area. 

4. Multiply the square root of the area by 1. 12837, ^^^ 
product is the diameter. 

5. Multiply the diameter by .8862, the product is the 
side of a square of equal area. 

6. Multiply the side of a square by 1.128, the product 
is the diameter of a circle of equal area. 

Application of the Rules to Practical Purposes. 
I. The diameter of a circle being 5 feet 6 inches, re- 
quired its circumference. 

5.5 X 3-1416 = 17.27880 feet, the circumference. 



Epitome of Mensuration. 8i 

2. A straight line or the circumference of a circle being 
17.27880 feet, required the circle's diameter corresponding 
thereto. 

17.27880 X -31831 = 5.5000148280 feet, diameter. 

3. The diameter of a circle is 9^^ inches ; what is its 
area in square inches ? 

9.375- z= 87.89, etc., X -7854 = 69.029, etc., inches, 
the area. 

4. What must the diameter of a circle be to contain an 
area equal to 69.029296875 square inches ? 

V69.02929, etc., = 8.3091 X 1. 12837 = 9.375, etc., or 
9% inches, the diameter. 

5. The diameter of a circle is 15J/2 inches; what must 
each side of a square be to be equal in area to the given 
circle? 

15.5 X .8862 = 13.73, etc., inches, length of side. 

6. Each side of a square is 13.736 inches in length; 
what must the diameter of a circle be to contain an area 
equal to the given square ? 

13.736 X 1. 128 = 15.49, etc., or 15}^ inches, the diameter. 

Any Chord and Versed Sine of a Circle being Oiven, to Find 
tlie Diameter. 

RuLE.-^DiV/c?^ the sum of the squares of the chord 
and versed sine by the versed sine; the quotient is the di- 
ameter of corresponding circle. 

7. The chord of a circle equals 8 feet and the versed 
sine equals i j^ ; required the circle's diameter. 

8- -f 1.5- = 66.25 -^ 1.5 = 44.16 feet, the diameter. 

8. In the curve of a railway I stretched a line 80 feet 
in length and the distance from the line to the curve I 
found to be 9 inches ; required the circle's diameter. 



82 Epitome of Mensuration. 

80- + .75- = 640.5625 ^ 2 = 320.28, etc., feet, the di- 
ameter. 

To Find the licngtli of Any Arc of a Circle, 

Rule. — From eight times the chord of half the arc 
subtract the chord of the whole arc, and one-third of the 
remainder zvill be the length, nearly. 

Required the length of an arc, the chord of half the arc 
being 8^ feet and chord of whole arc 16 feet 8 inches. 

8.5 X 8 = 68.0— 1 6.666 .:r= J_^^ :^ 13.778 cubic feet, 

o 
the length of the arc. 

To Find the Area of the Sector of a Circle. 

Rule. — Multiply the length of the arc by half the 
length of the radius. 

The length of the arc equals 9^2 inches and the radii 
equal each 7 inches ; required the area. 

9-5 X 3-5 = 33-25 inches, the area. 

To Find the Area of a Segment of a Circle. 

Rule. — Find the area of a sector whose arc is equal to 
that of the given segment, and if it be less than a semi- 
circle subtract the area of the triangle formed by the 
chord of segment and radii of its extremities; but if more 
than a semicircle add area of triangle to the area of the 
sector, and the remainder or sum is the area of the seg- 
ment. 

To Find the Area of the Space Contained Between Two 
Concentric Circles or the Area of a Circular Ring;. 

Rule i. — Miitlply the sum of the mside and outside 
diameters by their difference and by ./8j^; the product 
is the area. 



Epitome of Mensuration. 83 

Rule 2. — The difference of the area of the two cir- 
cles zvill be the area of the ring or space. 

Suppose the external circle equal 4 feet and the in- 
ternal circle 2y2 feet, required the area of space contained 
between them or area of a ring. 

4 + 2.5 = 6.5 and 4 — 2.5=1.5, hence, 6.5 X i-5 X 
.7854 = 7.65 feet, the area ; or. 

The area of 4 feet is 12.566; the area of 2.5 is 4.9081. 
( See table of areas of circles. ) 

12.566 — 4.9081 = 7.6579, the area. 

To Find the Area of an Ellipse or Oval. 

Rule. — Multiply the diameters togther and their prod- 
uct by .7854. 

An oval is 20 x 15 inches, what are its superficial con- 
tents ? 

20 X 15 X .7854 = 235.62 inches, the area. 

To Find tlie Circumference of an Ellipse or Oval. 

-^1:1^^.— Multiply half the sum of the tzvo diameters by 
3.1416 and the product wdl be the circumference. 

Example. — An oval is 20 x 15 inches, what is the cir- 
cumference. 
20 -\- 15 



2 

ference. 



17.5 X 3.1416= 54.978 inches, the circum- 



OF CYLINDERS. 

To Find tlie Convex Surface of a Cylinder. 

Rule.— Multiply the circumference by the hight or 
length, the product zvill be the surface. 

Example.— The circumference of a cylinder is 6 feet 



^4 Epitome of Mensuration. 

4 inches and its length 15 feet, required the convex 
face. 

6.333 X 15 = 94-995 square feet, the surface. 



OF CONES AND PYRAMIDS 

To Find tlie Convex Surface of a RiglU Cone or Pyrai 

Rule. — Multiply the circumference of the base &^ 
slant hight and half the product is the slant surface; i 
surface of the entire figure is required, add the urea 
base to the convex surface. 

Example. — The base of a cone is 5 feet diameteii 

the slant hight is 7 feet, what is the convex surface ? 

5 X 3-1416 = 15. 7Q circumference of the base 

I ^ 70 X 7 

-^^ (- = 54.95 square feet, the convex surface. 

To Find tlie Convex Surface of a Frustum of a Cone] 
Pyramid. 

Rule. — Multiply the sum of the circumference 
tzvo ends by the slant hight and half the product will b 
slant surface. 

The diameter of the top of the frustum of a co; 
3 feet, the base 5 feet, the slant hight 7 feet 3 inches 
quired the slant surface. 

2C 12 X 7 2^ 

9.42 + 15.7 = —^ <^-^- — 91.06 square feet, 

surface. 



Epitome of Mensuration. ^k 

OF SPHERES. 

To Fiud the Convex Surfaee of a Spliere or (;lobe. 

Rule. — Multiply tJie diameter of the spJiere by its eir- 
cumferenee and the product is its surface: or. 

Multiply the square of the diameter by ^.1416: the 
product is the surface. 

What is the convex surface of a glohe 6j^ feet in di- 
ameter ? 

6.5 X 3-1416 X 6.5 = 13273 square feet; or, 6.5= =r 
42.25 X 3-1416= 132.73 square feet, the convex surface. 



MENSURATION OF SOLIDS AND CAPACFriES 
OF BODIES. 

To Find the Solidity or Capaolty of Any Fl^nreH In the 
Cubloal Form. 

Rule. — Multiply the length of any one side by its 
breadth and by the depth or distance to its opf>osite side, 
and the product is the solidity in equal terms of measure- 
ment. 

Example. — The side of a cube is 20 inches : what is its 

soHdity? 

20 X 20X 20 = 8000 cubic inches, or 4.62^/) cuhk 

feet, nearly. 

A rectangular tank is in length 6 feet, in breadth 4' 2 
feet and its depth 3 feet; required its capacity in cubic 
feet ; also its capacity in United States standard gallons. 

6X4-5X3 = 81 cubic feet ; 81 X 1728 = 139.968 -f- 
231 = 605.92 gallons. 



t6 Epitome of Mensuration. 

OF CYLINDERS. 

To Find the Solidity of Cylinders. 

Rule. — Multiply the area of the base by the hight and 
the product is its solidity. 

Example. — The base of a cylinder is i8 inches and 
the product is its solidity. 

i8- X 7854 X 40 = 10,178.7840 cubic inches. 

To Find tlie Contents in Gallons or Cylindrical Vessels. 

Rule. — Take the dimensions in inches and decimal 
parts of an inch. Square the diameter^ multiply it by the 
hight, then multiply the product by .00^4 for wine gallons, 
or by .002/S^ for beer gallons. 

Example. — How many United States gallons will a 
cylinder contain whose diameter is 18 inches and length 
30 inches? 

18- X 30 = 9720 X .0034 = 33.04, etc., gallons. 



OF CONES AND PYRAMIDS. 

To Find tlie Solidity of a Cone or a Pyramid. 

Rule. — Multiply the area of the base by the perpen- 
dicular hight and one-third the product zvill be the solidity. 

Example. — The base of a cone is 2^ feet and the 
hight is 3^ feet, what is the solidity? 



Epitome of Mensuration. 87 

To Find the Solidity of the Frustum of a Cone. 

Rule. — To the product of the diameters of the ends 
add one-third the square of the difference of the diame- 
ters; multiply the sum by .7854 and the product zvill be the 
mean area between the ends, ivhich multiplied by the per- 
pendicular hight of frustum gives the solidity. 

Example. — The diameter of the large end of a frus- 
tum of a cone is 10 feet, that of the smaller end is 6 feet 
and the perpendicular hight 12 feet, what is its solidity? 

10 — 6 =: 4- = 16 -^ 3 = 5.333 square of difference of 
ends ; and 10X6 + 5.333 =: 65.333 X 7854 X 12 =: 
615.75 cubic feet, the solidity. 

To Find the Contents In U. S. Standard Gallons of the 
Frustum of a Cone. 

Rule. — To the product of the diameters, in inches and 
decimal parts of an inch, of the ends, add one-third the 
square of the difference of the diameters. Multiply the 
sum by the perpendicidar hight in inches and decimal parts 
of an inch and multiply that product by .00^4 for wine 
gallons, and by .002/8^ for beer gallons. 

Example. — The diameter of the large end of a frus- 
tum of a cone is 8 feet, that of the small-er end is 4 feet and 
the perpendicular hight 10 feet ; what are the contents in 
United States standard gallons ? 

96 — 48 = 48' = 2304 -^ 3 = 768 : 96 X 48 + 768 = 
5376 X 120 X .0034 = 2193.4 gallons. 

To Find the Solidity of the Frustum of a Pyramid. 

Rule. — Add to the areas of the tzvo ends of the frus- 
tum the square root of their product, and this suUi multi- 



8S Epitome of Mcnsuratioji. 

plied by oue-ihird of the perpendicular Jiight ivill give the 
solidity. 

Example. — What is the soHdity of a hexagonal pyra- 
mid, a side of the large end being 12 feet, one of the 
smaller ends 6 feet and the perpendicular hight 8 feet? 

374.122 + 93.53 = V34,99i.63 = 590.811 ; 374-122 + 

93.53 ~ 590.811 = - — -4 3 _ 2822.568 cubic feet, 

o 
solidity. 

To Find the Solidity of a Splierc. 

Rule. — Multiply the cube of the diameter by .52^6 
and the product is the solidity. 

Example. — What is the solidity of a sphere, the di- 
ameter being 20 inches ? 
20^ = 8000 X -5236 = 4188.8 cubic inches, the solidity. 



TABLES, RULES AND RECIPES. 



BLACK SHEET IKON. 

Black Sheets are rolled to the following Standard Gauges adopted 
by the United States, taking eftect July 1, 1893. 

, THICKNESS. N r WEIGHT. ^ 

Approxi- 

Aiwroximate mate thick- Weight per Weight per 

thickness ness in dec- square foot square toot 

Number infractions imal parts in ounces in pounds 

of oau-e of an inch, of an inch, avoirdupois, avoirdupois. 

10 " " 9-04 .140625 90 5.025 

IV I-S 125 80 5. 

li 7-(;4 ".109375 70 4.375 

|q 3-32 .09375 00 3.<o 

11 :::::::: 5-04 .078325 50 3.120 

i^ 1)-128 .0703125 45 2.8125 

\% l-KJ .0025 40 2.0 

l': :::::: ::::::: 9-100 05025 30 2.20 

1« 1-20 .05 32 2. 

lo' ■:::::::::::: 7-100 .04375 25 1.70 

20 3-80 .0375 24 1.50^ 

i?::::::::::::::n-32o .034375 22 \^ 

09 1-32 .03125 20 1.2o 

23 :::::: 9-320 .028125 is 1.120 

94 :: 1-40 .025 16 1. 

9^ 7-320 .021875 14 .8<o 

% :::::: 3-100 .01875 12 .70 

St : ....11-040 .0171875 11 -6875 

5o 1-04 .01.5025 10 -025 

i :::::: lluo .0140025 . 9 .5620 

00 . 1-80 .0125 8 .5 

§V 7-040 .0109375 7 -43 g 

I2 :::::: 13-1280 .0101.5025 oy^ .40025 

A variation of 2V2 per cent, either way is allowed. 

Plate Iron. 

The following table gives the weight per square foot 
for iron plates 1-16 inch up to /. inch thick. 

Thickness. Weight in lbs. Thickness. Weight in lbs. 

l-^« ^.'nn 38 15.00 

1-8 5-00 7L 17.50 

3-lS J-^2 12 20.00 
1.4 10.00 1-^ 



Tables, Rules and Recipes. 
WEIGHT OF SHEET LEAD. 

The thickness of lead is in common determined or understood by the 
weight, the unit being that of a square or superficial foot ; thus : 

4 lbs. lead is 1-16 inch in thickness ; 6 do. 1-10 do. ; 71/^ do. 1-8 do. ; 11 
do. 3-16 do. ; 15 do. 1-4 do. 



DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF A 

POUND. 



03125 


Vs oz. .28125 


41/2 oz. .53125 


8% oz. .78125 


I2y2 oz 


0625 


1 ' 


.3125 


5 


.5623 


9 ' 


.8125 


13 " 


09375 


IV2 ' 


.34375 


5M. 


.59375 


91/2 ' 


.84375 


i3y2 " 


125 


2 


.375 


6 


.625 


10 ' 


.875 


14 " 


.15625 


21/2 ' 


.40625 


61/2 


.65625 


IOV2 ' 


.90625 


i4y2 •* 


1875 


3 ' 


.4375 


7 


.6875 


11 ' 


.9375 


15 " 


.21875 


31/2 ' 


.46875 


7y2 


.71875 


iiy2 ' 


.96875 


i5y2 " 


.25 


4 ' 


.5 


8 


.75 


12 ' 


1. 


16 " 



DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF AN 
INCH WHEN DIVIDED INTO 32 PARTS; LIKEWISE THE 
DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF 
A FOOT. 





Parts of an 




Parts of an 




Parts ot 


Decimals. 




inch. 


Decimals. 


inch. 


Decimals. 


a foot. 


.03125 


1-32 




.53125 


y. and 1-32 


.01041 


Vs 


.0625 


1-16 




.5625 


¥2 and 1-16 


.02083 


Vi 


.09375 


3-32 




.59375 


Vo and 3-32 


.03125 


% 


.125 


ys 




.625 


% 


.04166 


V2 


.15625 


Vs 


and 1-32 


.65625 


5/s and 1-32 


.05208 


% 


.1875 


Vs 


and 1-16 


.6875 


% and 1-16 


.0625 


% 


.21875 


Vs 


and 3-32 


.71875 


% and 3-32 


.07291 


Vs 


.25 


Vi 




.75 


% 


.0833 


1 


.28125 


y* 


and 1-32 


.78125 


% and 1-32 


.1666 


2 


.3125 


V4 


and 1-16 


.8125 


% and 1-16 


.25 


3 


.34375 


% 


and 3-32 


.84375 


% and 3-32 


.3333 


4 


.375 


% 




.875 


% 


.4166 


5 


.40625 


% 


and 1-32 


.90625 


Vs and 1-32 


.5 


6 


.4375 


% 


and 1-16 


.9375 


% and 1-16 


.5833 


7 


.46875 


% 


and 3-32 


.96875 


Vs and 3-32 


.6666 


8 


.5 


% 




1. 


1 inch. 


.75 

.8333 

.9166 


9 

10 
11 



Tables, Rules and Recipes. 91 



TO ASCERTAIN THE WEIGHTS OF PIPES OF VARIOUS METALS, 
AND ANY DIAMETER REQUIRED. 



Thick. 


Wrought 






Thick. 


Wrought 






Inch. 


iron. 


Copper. 


Lead. 


Inch. 


iron. 


Copper. 


Lead. 


1-32 


.326 


.£8 


.483 


5-32 


1.627 


1.9 


2.417 


1-16 


.653 


.76 


.967 


3-16 


1.95 


2.28 


2.9 


3-32 


.976 


1.14 


1.45 


7-32 


2.277 


2.66 


3.383 


1-8 


1.3 


1.52 


1.933 


1-4 


2.6 


3.04 


3.867 



Rule. — To the interior diameter of the pipe, in inches, 
add the thickness of the metal; multiply the sum by the 
decimal number opposite the required thickness and under 
the vietaTs name ; also by the length of the pipe in feet; 
and the product is the weight of the pipe in pounds. 

I. Required the weight of a copper pipe whose in- 
terior diameter is 2^2 inches, its length 20 feet, and the 
metal % inch in thickness. 

2.25 + .125 = 2.375 X 1.52 X 20 = 72.2 pounds. 

WEIGHT OF GALVANIZED SHEETS. 

Ounces per Ounces per Ounces per 

square foot. square foot. square foot. 

No. 14 52V, No. 20 261/2 No. 26 141/2 

No. 15 471/2 No. 21 241/2 No. 27 I31/2 

No. 16 42i/> No. 22 22i/> No. 28 I21/2 

No. 17 381/2 No. 23 201/2 No. 29 II1/2 

No. 18 341/2 No. 24 I8I/2 No. 30 10l^ 

No. 19 301/2 No. 25 I6I/2 

ORDINARY DIMENSIONS OF GALVANIZED SHEETS. 

Widths 40 38 36 34 32 30 28 26 24 22 20 

Gauges. Lengths. 

No. 14 96 96 96 96 96 96 96 96 96 

Nos. IC) to 22 120 120 120 120 120 120 120 120 120 120 120 

Nos. 23 and 24. . . 96 96 96 96 108 120 120 120 120 108 108 

Nos. 25 to 28 96 96 108 120 120 120 120 108 108 

Nos. 29 and 30 96 96 96 96 .. .. 



92 Tables, Rules and Recipes. 

WEIGHT PER FOOT OF LEAD PIPE. 

Inside AAA AA ABC D E 

diam- Brook- Ex. Ex. • Foun- 

eter. Ivii. strong. Strong. Medium. Light. light. tain. 

Ins. Lb. Oz. Lb. Oz. Lb. Oz. Lb. Oz. Lb. Oz. Lb. Oz. Lb. Oz. 

% 1 12 1 8 1 4 1 12 10 1 7 

7-16 1 13 

1/, 3 2 1 12 1 4 1 12 9 

5/s 3 8 2 12 2 8 2 1 8 1 12 

% 4 12 3 8 3 2 4 1 12 1 4 1 

1 G04 12 4 03 42 82 1 8 
IVt 6 12 5 12 4 12 3 12 3 2 8 2 
IV, 8 8 7 8 f) 8 5 4 4 3 8 3 
lyl 10 8 8 7 6 5 4 

2 11 12 9 S 7 G 4 12 . . . 



Tables, Rules and Recipes. 



93 



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Tables, Rules and Recipes. 









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rHrHrHrHCJ 



OOO 
OCOJO 
COCOTt^ 



P.O Cl TtH CO X 

ggcococococo 
^66666 

cHi5 1*5 ;^ ;^ ^ 



Tables, Rules and Recipes. 



95 



O C^l CI 05 _ _ _ 00 C5 _ 00 M «£> r^ T)< 00 -^ tn rQ 

C^ -*■ lO lO 1^^ <X> CO t- ^. OS t- Ol C/^ C-. Oi O 'M o 3 

CI O O C<J ifi OC C^i CD O^' CO M r-i O O C^ 50 •<* CO CKi ^ 

• . -^ ■<*! Tj< LO lO in CO t- 00 C~ 00 D~ 00 00 Ol rH Oi Q 

O I>;Oit>.00_M_OCI>;CO(M_-*C<)-*CT5fOCO ^ 

"^^ . ^ COfOTt<Tf^L0 10COC-COt-COt-C~OC(S^- m 

M is 

'O 

O irt(Mt~-* 00 <M C^COfOOO?0 Tf<Tti 

2 c9 o t4 ^" CD oi CI Tt< L-^ ■*' o cd C I>^ ^' CO M -^ 00 S 

'^ "^ S CO CO CV3 CO ^ f ^ in CD lO CD Ln CD CO C-- S CO o 

m cscocDt— im ^. irtCDiMC<i i— ir^oicocD -_ 

95 o S oOrHcocDooT-Hcoaiiriooincooii-iot^c^i o 

"^ . . ^ c: CO coco ■*■*-* ift -^m in mm CD I- CD lo 

o e<;-^j<iooc _c^icoaiinooT-HT-Ht---^o:T-4C5 3 

L3 00 o «5o6o(M"int-'a5;g|ocoooococ^aioco O 

'^ . . (Mcicoc-3cococo-^m-*Lnrt<LOir2mt-u:i j^ 

10 ^ i.ocD-*'*i-*'*coeo-^_co_c<iiM 00 (J, 

S S o P-5 Cpior-cirHcoi'ogiriciincoc^'t^cocor-i ta 

• • n '^3 c-i ivi cj CO CO CO ^ '^ CO •* ^ -1< tt u's CO o 2' 
'-' W g 

o ^ ooinc^ioocsirt irsi-KMCD coco !> 

i2 S O !l2 I-HCJ^COC^OSTHCOOIOOGCCOCJOOCDIO ^ 

CO 

CO oiijs cDcoas-^-^iocoo-it-^t^occ^ic- o) 

ZS M § 05 o6oc<icoincDoocicdT-icO'*oot-cooi-i ^ 

^ ^. =C r -, ,-( (M c^q (M (M (M (M CO CO CO CI e>0 CO CO Tf U5 rj< O 

C^l '~' OOCOCO lOOSC^OO-*!— lOaOO-rfCDTf US 

g3 S r? cDodair-HiricoLOodc^]o6c^o-<i-"coo6incD 

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00 ^ t- iHTt<C~a5 (M-*CDtH ^iH-rfCOCOOl 

£J '§ 2J O -*■ CO t>^ 00 oi O <m' LO 00 '^ 00 t-^ O oi CO oi ,-H O 

■-I -^ '-'. ►-( i-H r-1 r-1 iH T-l Csl ffq Cq Cq CQ IM CJ CO CI C; CO CO ^ 

-^ ;^ CDt-t-OOCi OiCOCO _THr^0O(MOO0O-* O 

EJ S !^ "^ c^dcoTt^incdodocSr-J-rj^T-H-^coiftLtrodcoi^^ "^ 

O tj l-'O'VT'CJC^li-l ,00 _COCOTHCOir5 c^ioo d 

2 r2 r^ ^ o^c-ico'*<irti6o6c5t-^oai,-Hr-!^ooe<i ^ 

00 M -^CqaiOOCO-^T-l-THT-lt- (MC-TOOmrH-^ ^ 

• o « 

CD pH -^i-iOOlOCq CD-^iCvlr-lT-J-^CqoOMlftCO M 

°° S o ^-1 ocoJaior-icica'J'CD^'coint-cDaicio? "O 

T»< ■^ coa5irtT-it--*OiLOr-;cq ^-^cicot^iooo O 

'"" £5 o t>^ t- 06 oi oj o o ci ^Vi '^ CO -th ^ CD oi in ^ 

^^^^^^^^^^^^ g 

CI cocji-e<a;'*< _inoqcqcDr-HCOaico'*'_c-jc-; ^ 

^ i§ g cocot>^t>^o6aia5ociocii-icici-rf"coco +-> 

'^ o 

o cico toos-^^ooci _i>-<jiiftco-<*<o5aico -^ 

i^ ^ g iniocDcocot-^t-^odooooiaJoor-ico'T-i " 

. CqcDOiCOCOOCOCJi-J _ _t-;CD-*COCOi-; W) 

tk o o S ■*' ^^' in in CO CO t-^ 00 t-^ 00 f>^ 00 oo' oi T-; oj ^ 

CO a; cj o ^"^ '"' « 

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5>m^S.5r7^ rfCOOOOCTTf^COCOCOOO^COOCOOOCl _rt 

[2;^'«^+-'-'M cicqcicococticoc.oco^'f*'-!r-<r^L:5io >« 



96 



Tables, Rules and Recipes. 



RELATIVE WEIGHTS OF ALUMINUxM AND 
COPPER SHEETS, 

ROLLED ALlJUIlMTin has a specific gravity of 2.72. One cubic foot 
weighs IGGyViny lbs. One square foot of one inch thick weighs WiVor. lbs. 
Rolled Copper is 3.283 times heavier than similar sections of Rolled 
Aluminum. 



o 


m 


C 


, 


a 


a ^ 


a 


fl <*-i 


C3 


ti 


a a '*:' 


g 


f= V. 


^ 


Xi 


0.1 


a 








•- 




-H 




< 




- 






S 


- i 


^ 


-^ a 


^_j 


*-' a 


^ 


-^ a 


-1.J -1- 


' a 


^^ 


t:^ a 


^ 




8 


« % 


^ 


•=3 s 


^ 


•a s 


A 


-a S 


A -Ob 


a 


■? s 


M 


"5 




V. ^ 


bt, 


be 5 


bX) 


.^fl 


.^ 


^a 


be be g 


be 


^a 




a 


o 

1 


is 


^1 


00 "a 












^-8 


a 


§, 


•Sd 




ii 


«:: 


« o 


t ^<^ 


«o| 


><^ 


^ o| 





'St 





^o-g 


C3 

be 


M .2 


s 

^ 




'a 


r-l CO 


•- ^ o 


^.2 






(£> <X> -p 00 

CO ^ C^ 02 ~ ■* CC 


13 '^ 




fl rH 


u 


;-, 


m fl 


W T 


5; t» r3 


w fl i 


w fl 


02 fl a; 


w r! _2 


c 9i 


M a 


t» c S 


1 


i: 


s. 


S| 


4-i " 


1 o 


a n, O 


lil 


% 


t; = a 

S C> oj 


? 1^ 


p 


Si 


$|« 


.a o 


^ 


N a 


^ a 


5 a^^ a 


^ ace 


^ o- 


^ a CO 


Si —X 


a w^ w. 


cj aw 


m 


H 


o 


O 


CO 


M 


m 


TJI 


02 


tZ2 


yj a 


CO w 


?,5 


.00587 


4 


1.22 


1.16 0.35 2 


0.61 


3.12 


0.96 


4.50 


1.38 


6 


1.83 


33 


.00806 


6 


1.83 


1.75 0.53 3 


0.92 


4.68 


1.43 


6.75 


2.06 


9 


2.75 


31 


.0107 


8 


2.44 


2.33 0.71 4 


1.22 


6.25 


1.91 


9 


2.75 


12 


3.63 


29 


.0131 


10 


3.05 


2.91 0.89 5 


1.53 


7.81 


2.38 


11.25 


3.43 


15 


4.57 


27 


.0161 


12 


3.66 


3.50 1.07 6 


1.83 


9.37 


2.86 


13.50 


4.12 


18 


5.49 


26 


.OISS 


14 


4.27 


4.08 1.25 7 


2.14 


10.93 


3.33 


15.75 


4.80 


21 


6.40 


24 


.0215 


16 


4.88 


4.66 1.42 8 


2.44 


12.50 


3.81 


18 


5.49 


24 


7.32 


23 


.0242 


18 


5.49 


5.25 1.60 9 


2.75 


14.06 


4.29 


20.25 


6.17 


27 


8.23 


22 


.0269 


20 


6.10 


5.83 1.78 10 


3.05 


15.62 


4.76 


22.50 


6.86 


30 


9.14 


21 


.0322 


24 


7.32 


7 


2.14 12 


3.66 


18.75 


5.72 


27 


8.23 


36 


11.00 


19 


.0430 


32 


9.75 


9.33 2.85 16 


4.88 


25 


7.62 


36 


11.00 


48 


14.70 


18 


.0535 


40 


12.20 


11.66 3.56 20 


6.10 


31.25 


9.52 


45 


13.75 


60 


18.30 


16 


.0645 


48 


14.65 


14 


4.27 24 


7.32 


37.50 


11.45 


54 


16.50 


72 


22.00 


15 


.07.54 


56 


17.10 


16.33 4.98 28 


8.-53 


43.75 


13.35 


63 


19.20 


84 


25.60 


14 


.0860 


64 


19.50 


18.66 5.69 32 


9.75 


50 


15.30 


72 


21.95 


96 


29.30 


13 


.095 


70 


21.35 






35 


10.70 


55 


16.80 


79 


24.10 


105 


32.00 


12 


.109 


81 


24.70 






401/2 


12.40 


63 


19.20 


91 


27.75 


122 


37.20 


11 


.120 


89 


27.15 






. 441/3 


13.60 


70 


21.35 


100 


30.50 


134 


.40.85 


10 


.134 


100 


30.50 






50 


15.30 


78 


23.80 


112 


34.20 


150 


45.70 


9 


.148 


110 


33.55 






55 


16.80 


S6 


26.20 


124 


37.80 


165 


50.30 


8 


.165 


123 


37.50 






61 


18.60 


96 


29.30 


138 


42.10 


184 


56.10 


7 


.180 


134 


40.85 






67 


20.40 


105 


32.00 


151 


46.00 


201 


61.30 


6 


.203 


151 


46.00 






751/2 


23.00 


118 


86.00 


170 


51.80 


227 


69.20 


5 


.220 


164 


50.00 






. 82 


25.00 


.'28 


39.00 


184 


56.10 


246 


75.00 


4 


.238 


177 


53.95 






881/2 


27.00 


138 


42.10 


199 


60.70 


266 


81.10 


3 


.259 


193 


64.30 






96 


29.30 


151 


46.00 


217 


66.10 


289 


88.10 


2 


.284 


211 


67.95 






1051A 


32.20 


165 


50.30 


238 


72.50 


317 


96.60 


1 


.300 


223 


77.10 






IIIV2 


34.00 


174 


53.10 


251 


76.50 


335 


102.20 





.340 


253 








1261/. 


38.60 


198 


60.40 


285 


86.90 


380 


116.00 



One ounce per square foot aluminum sheet is 0.0044 inch thick s^^ 
corresponds to about No. 37 B. & S. gauge. 



Tables, Rules and Recipes. 



97 



SHEET COPPER. 



Official table adopted by the Association of Copper Manufac- 
turers of the United States. 

Rolled copper has specific gravity of 8.93. One cubic foot 
weighs 558^"/iooo pounds. One square foot, of 1 inch thick, weighs 
46^Vwo pounds. 



bi)_ .5 cs 

<!i m -J, 02 — "S 

t* a; a> ^ « in 

S ? p ^.S 

35 00537 

33 00806 

31 0107 

29 0134 

27 0161 

26 0188 

24 0215 

23 0242 

22 0269 

21 0322 

19 0430 

18 0538 

16 0645 

15 0754 

14 0860 

13 095 

12 109 

11 ... .120 

10 134 

9 148 

8 165 

7 c. . .180 

6 203 

5 220 

4 238 

3 259 

2 . .284 

1 300 

340 





00 M 


X w 


CC 


Cf x 


of w 


• 


rfi^ 


TtH^ 


^:2 


l-£ 


l-.^ 


U O 


^'II 


Ml! 


x""! 


X "" 


X "■ 


<x> o 


.t^.2 


r^B 


O.S 


CO .9 


00.9 


rr, O 


•— 1 ^ 


(N-M 


CO 4^ 


CO-M 


TtH^ 


g u 


cc.f3 


Ul^ 


03^ 


M^ 


02 -a 


o rt 


■^ tt) 


4-^ bD 


-M W) 


■M btl 


4-. 6« 




O/.-, 


0).-- 


gj.— 


OJ— . 


0/.- 


fi ^ 


0^ <u 


O) ai 


O) o; 


O) O' 


O) 0^ 


^ ^ 


- ^ 


Si ^ 


- ^ 


-a p: 


•^ p: 


o 


1/2 


m 


VI 


Ui ^ 


as "^ 


4 


1.16 


2 


3.12 


4.50 


6 


6 


1.75 


3 


4.68 


6.75 


9 


8 


2.33 


4 


6.25 


9 


12 


10 


2.91 


5 


7.81 


11.25 


15 


12 


3.50 


6 


9.37 


13.50 


18 


14 


4.08 


7 


10.93 


15.75 


21 


16 


4.66 


8 


12.50 


18 


24 


18 


5.25 


9 


14.06 


20.25 


27 


20 


5.83 


10 


15.62 


22.50 


30 


24 


7 


12 


18.75 


27 


36 


32 


9.33 


16 


25 


36 


48 


40 


11.66 


20 


31.25 


45 


60 


48 


14 


24 


37.50 


54 


72 


56 


16.33 


28 


43.75 


63 


84 


64 


18.66 


32 


50 


70 


96 


70 




35 


55 


79 


105 


81 




401/2 


63 


91 


122 


89 




441/2 


70 


100 


134 


100 


.... 


50 


78 


112 


150 


110 


.... 


55 


86 


124 


165 


123 




61 


96 


138 


184 


134 


.... 


67 


105 


151 


201 


151 




751/2 


118 


170 


227 


164 


.... 


82 


128 


184 


246 


177 




88 1/2 


138 


199 


266 


193 


.... 


96 


151 


217 


289 


211 




1051/0 


165 


238 


317 


223 




1111/2 


174 


251 


335 


253 


.... 


1261/2 


198 


285 


380 



TABLKS 

OF THE 

CIRCUMFERENCES OF CIRCLES, 

TO THE 

Nearest Fraction of Practical Measurement; 

ALSO, 

the areas of CIRCLES, IN INCHES AND DECIMAL PARTS, 

LIKEWISE IN FEET AND DECIMAL PARTS, AS 

MAY BE REQUIRED. 



Rules that may render the following tables more gen- 
erally useful. 

1. Any of the areas in inches, multiplied by .052, or 
the areas in feet multiplied by 7.48, the product is the num- 
ber of gallons at i foot in depth. 

2. Any of the areas in feet, multiplied by .03704, the 
product equals the number of cubic yards at i foot in 
depth. 

Dia. in Circum. Area in Side of Dia. in Cir. in Area in Area in 

inch. in inch. sq. inch. — sq. inch. ft. in. sq. inch. sq. ft. 

1-16 .196 .0030 .0554 1 in. 3% .7854 % 

1-8 .392 .0122 .1107 1% ^V2 -9940 % and 3-32 

3-16 .589 .0276 .166] 1^4 SVs 1.227 1 in. 

1-4 .785 .0490 .2115 1% 41^ 1.484 1 3-16 

5-16 .981 .0767 .2669 IVa 4% 1.767 1 5-16 

3-8 1.178 .1104 .3223 1¥^ 5% 2.074 1 7-16 

7-16 1.374 .1503 .3771 1% SVg 2.405 1 9-16 

IVs 5% 2.761 1 11-16 

1-2 1.570 .1963 .4331 2 in. 6% 3.141 1% 

9-16 1.767 .2485 .4995 2% 6% 3.546 IVs 

5-8 1.963 .3068 .5438 21/4 7 3.976 2 in 

11-10 2.1.59 .3712 .6093 2% 7% 4.430 2y8 ' 

3-4 2.356 .4417 .6646 2i/^ 7% 4.908 2 3-16 

13-16 2.552 .5185 .7200 2>s 814 5.412 2 .5-16 

7-8 2.748 .6013 .77.54 2% 8% 5.939 2 7-16 

15-16 2.945 .6903 .8308 2ys 9 6.491 2 9-16 



7 ablcs, Rules and Recipes. 



99 



Ilia. 


in. Cir 


'. Area in ! 


Side of 


Dia. in 


Ci 


r. in 


Area in 


Area in 


mch 


. in incli sq. 


inch. 


= sq. 


inch. 


ft, 


. in. 


sq. inch. 


sq. ft. 


3 in 


9% 


7.1 


068 2 


;% 


10 in. 


2 


7% 


78.540 


.5497 


3Vs 


9% 


7. 


609 2% 


loys 


2 


7% 


80.515 


.5636 


3V4 


.1^34 


8. 


295 2y8 


101/4 


2 


8% 


82.516 


.5776 


3% 


lOfs 


8.! 


.>4t; 3 


in. 


10% 


2 


81/2 


84.540 


.5917 


31/2 


11 


9.G21 31/8 


101/0 


2 


8% 


86.590 


.6061 


3^/H 


11% 


10. 


320 314 


M 


2 


9% 


88.664 


.6206 


3% 


11% 


11.044 3% 


2 


9% 


90.762 


.6353 


BVs 


121/s 


11. 


793 3 


7-16 


loys 


2 


10% 


92.855 


.6499 


Dia. i 


in Ci 


r. in 


Area in 


Area in 


11 in. 


2 


10% 


95.033 


.6652 


iucl] 
4 in. 

t^ 

4.% 
41/2 

4% 




in. 

01/0 
0% 
1% 
1% 

2y8 
21/2 

2Vh 


sq. inch. 
12..J6G 
13.364 
14.186 
15.033 
15.904 
16.800 
17.720 


sq. ft. 
.0879 
.0935 
.0993 
.1052 
.1113 
.1176 
.1240 


iiys 
1114 
11% 
iiy> 

ill 

11% 


2 
2 
2 
3 
3 
3 
3 


10% 

0% 

1 


97.205 
99.402 
101.623 
103.869 
106.139 
108.434 
110.753 


.6874 
.6958 
.7143 
.7290 
.7429 
.7590 
.7752 


4^/, 




31/4 


18.665 


.1306 


12 in. 


3 


1% 


113.097 


.7916 


5 in. 




l^ 


19.635 


.1374 


ViYf 


3 


2 


115.466 


.8082 


5y8 




20.629 


.1444 


}~.Y^ 


3 


^y? 


117.859 


.8250 


5 1/4 




41/2 


21.647 


.1515 


12% 


3 


2% 


120.276 


.8419 


il 




4"/s 


22.690 


.1588 


H>^ 


3 


3y4 


122.718 


.8590 




5^ 


23.758 


.1663 


12% 


3 


3% 


125.185 


.8762 


5% 




5% 


24.850 


.1739 


12% 


3 


4 


127.676 


.8937 


5% 

5"/8 




e' 


25.967 


.1817 


12% 


3 


4% 


130.192 


.9113 




6% 


27.108 


.1897 






















13 in. 


3 


4% 


132.732 


.9291 


6 in. 




6% 


28.274 


.1979 


13% 


3 


51/4 


135.297 


.9470 


61/8 




7y4 


29.464 


.2062 


131/4 


3 


5% 


137.886 


.9642 


61/4 




7% 


30.679 


.2147 


13% 


3 


6 


140.500 


.9835 


6% 




8 


31.919 


.2234 


131/2 


3 


6% 


143.139 


1.0019 


6% 




8% 


33.183 


9392 


13% 


3 


6% 


145.802 


1.0206 


6% 




8% 


34.471 


;2412 


13% 


3 


7% 


148.489 


1.0294 


6% 




91/8 


35.784 


.2504 


13% 


3 


7% 


151.201 


1.0584 


6% 




91/2 


37.122 


.2598 






















14 in. 


3 


7% 


153.938 


1.0775 


7 in. 




10 


38.484 


.2693 


•14% 


3 


8% 


156.699 


1.0968 


7% 




}^^ 


39.871 


.2791 


141/4 


3 


8% 


159.485 


1.1193 


714 




10% 


41.282 


.2889 


14% 


3 


9% 


162.295 


1.1360 


7% 




V.Y^ 


42.718 


.2900 


141/0 


3 


91/2 


165.130 


1.1569 


71/0 




IIV, 


44.178 


.3092 


14% 


3 


9"/8 


167.989 


1.1749 


Z!4 




11% 


45.663 


.3196 


14% 


3 


10^ 


170.873 


1.1961 


7I 




2 


0% 
0% 


47.173 
47.707 


.3299 
.3409 


14% 


3 


10% 


173.782 


1.2164 


8 in 


'2 


IH 


50 265 


.3518 


15 in. 


3 


11% 


176.715 


1.2370 


8% 


9 


IVo 


51 848 


3629 


15% 


3 


11% 


179.672 


1.2577 


81/4 
8% 


2 
2 


lYs 
214 
2% 


53.456 

55.088 


.■3741 
3856 


I5y4 

15% 


3 
4 


11% 

014 


182.654 
185.661 


1.2785 
1.2996 


SVi 


2 


56.745 


.3972 


151/2 


4 


0% 


188.692 


1.3208 


8% 


2 


3' 


58.426 


.4089 


l^f? 


4 


1 


191.748 


1.3422 


8% 


9 


3% 


60.132 


.4209 


15% 


4 


1% 


194.828 


1.3637 


8-/8 


2 


3% 


61.862 


.4330 


15% 


4 


1% 


197.933 


1.3855 


Oiri. 


2 


414 


63.617 


.4453 


16 in. 


4 


214 


201.062 


1.4074 


91^ 


2 


478 


65.396 


.4517 


16% 


4 


2% 


204.216 


1.4295 


9^4 


2 


5 


67.200 


.4704 


161/4 


4 


3 


207.394 


1.4517 


0% 


2 


5% 


69.029 


.4832 


16% 


4 


3% 


210.597 


1.4741 


91A 


2 


5% 


70.882 


.4961 


leys 

16% 


4 


II 


213.825 


1.4967 


0% 


2 


61/4 


72.7.59 


.5093 


4 


217.077 


1.5195 


9% 


2 


6ys 


74.662 


.5226 


16% 


4 


4% 


220.353 


1.5424 


978 


2 


7 


76.588 


.5361 


16% 


4 


5 


223.654 


1.5655 



100 



Tables, Rules and Recipes. 



Dia. in 
inch. 



Cir. in 
ft. in. 



Area in 
sq. inch, 



17 in. 


4 


5% 


226.980 


ITi/s 


4 


5% 


230.330 


17% 


4 


6% 


233.705 


17% 


4 


61/2 


237.104 


i7y2 


4 


6% 


240.528 


17% 


4 


7% 


243.977 




4 


7% 


247.450 


17% 


4 


8% 


250.947 


18 in. 


4 


8% 


254.469 


ISVs 


4 


8% 


258.016 


181/4 


4 


91/4 


261.587 


18% 


4 


9% 


265.182 


18% 


4 


lOVs 


268.803 


18% 


4 


10% 


272.447 


18% 


4 


10% 


276.117 


18% 


4 


111/4 


279.811 


19 in. 


4 


11% 


283.529 


191/8 


5 





287.272 


191/4 


5 


01/2 


291.039 


19% 


5 


0% 


294.831 


lOVa 


5 


11/4 


298.648 




5 


1% 


302.489 


19% 


5 


2 


306.355 


19% 


5 


2% 


310.245 


20 in. 


5 


2% 


814.160 


20% 


5 


3y4 


318.099 


201/4 


5 


3% 


322.063 


20% 


5 


4 


326.051 


201/2 


5 


4% 


330.064 


20% 


5 


4% 


334.101 


20% 


5 


5% 


338.163 


20% 


5 


51/2 


342.250 



21 in. 

21% 
2114 
21% 
211/2 
21% 
21% 
21% 

22 in. 

22% 
2214 
22% 
221/, 
22% 
22% 
22% 

23 in. 

23% 
231/1 
23% 
23% 
23% 
23% 
23% 



5 5% 
5 6% 



6% 

7% 
71/0 
7% 
81/4 
8% 

9% 

91/2 

9% 

101/4 

5 10% 

5 11 

5 111/2 

5 11% 



6 01^ 

6 

6 



UV4 

0% 

6 1% 
" 1% 

21/4 
2% 



6 
6 
6 
6 3 



346.361 
350.497 
354.657 
358.841 
363.051 
367.284 
371.543 
375.826 

380.133 
384.465 
388.822 
393.203 
397.608 
402.038 
406.493 
410.972 

415.476 
420.004 
424.557 
429.135 
433.737 
438.363 
44,3.014 
447.690 



Area in 
sq. ft. 
1.5888 
1.6123 
1.6359 
1.6597 
1.6836 
1.7078 
1.7321 
1.7566 

1.7812 
1.8061 
1.8311 
1.8562 
1.8816 
1.9071 
1.9328 
1.9586 

1.9847 
1.9941 
2.0371 
2.0637 
2.0901 
2.1172 
2.1443 
2.1716 

2.1990 
2.2265 
2.2543 
2.2822 
23103 
2.3386 
2.3670 
2.3956 

2 4244 

2.4533 
2.4824 
2.5117 
2.5412 
2.5708 
2.6007 
2.6306 

2.6608 
2.6691 
2.7016 
2.7224 
2.7632 
2.7980 
2.8054 
2.8658 

2.8903 
2.9100 
2.9518 
2.9937 
3.0129 
3.0261 
3.0722 
3.1081 



Dia. in 
ft. in. 



Cir. in 
ft. in. 





01/4 
01/2 
0% 

1 

114 
iy2 
1% 

2 

21/4 

2% 

2% 

3 

31/t 

31/2 

3% 

4 

41/4 
41/2 
4% 
5 

51/4 
51/2 
5% 

6 

6% 
61/2 
6% 
7 

71/4 
71/2 
7% 



81/t 

SVa 

8% 

9 

91/4 

91/0 

9% 

10 

101/4 
101/2 
10% 

11 

111/4 
ni/2 
11% 



0% 
01/2 
0% 

IV4 
11/2 
1% 



3% 
4% 

4% 
5% 

6% 

71/4 

8% 
9% 

loyo 

111/4 



0% 

1% 
2% 
3% 

3% 
4% 

5y2 
614 
7 

7% 

8% 

9y2 

ioy4 
11 

11% 

0% 
1% 
2% 
2% 
3% 

4% 
5% 
eyg 

6% 
7% 
81/3 
914 
10 

10% 

111/0 

0% 

m 
1% 
2% 
31/2 

41/4 

5 

5% 

6% 

7y2 
81/4 
9 

9% 
101/2 



Area in 

sq. inch. 

452.290 

461.864 

471.436 

481.106 

490.875 

500.741 

510.706 

520.769 

530.930 
541.189 
551.547 
562.002 
572.556 
583.208 
593.958 
604.807 

615.753 
626.798 
637.941 
649.182 
660.521 
671.958 
683.494 
695.128 

706.860 
718.690 
730.618 
742.644 
754.769 
766.992 
779.313 
791.732 

804.249 
816.865 
829.578 
842.390 
855.300 
868.308 
881.415 
894.619 

907.922 
921.323 
934.822 
948.419 
962.115 
975.908 
989.800 
1003.79 

1017.87 
1032.06 
1046.35 
1060.73 
1075.21 
1089.79 
1104.46 
1119,24 



Area in 
sq. ft. 
3.1418 
3.2075 
3,2731 
3.3410 
3.4081 
3.4775 
3.5468 
3.6101 

3.6870 
3.7583 
3.8302 
3.9042 
3.9761 
4.0500 
4.1241 
4.2000 

4.2760 
4.3521 
4.4302 

4.5083 
4.5861 
4.6665 
4.7467 

4.8274 

4.9081 
4.9901 
5.0731 
5.1573 

5.2278 
5.3264 
5.4112 
5.4982 

5.5850 
5.6729 
5.7601 
5.8491 
5.9398 
6.0291 
6.1201 
6.2129 

6.3051 
6.3981 
6.4911 
6.5863 
6.6815 
6.7772 
6.8738 
6.9701 

7.0688 
7.1671 
7.2664 
7.3662 
7.4661 
7.5671 
7.6691 
7.7791 



Tables, Rules and Recipes. 



lol 



D= 


a. in 


Cir 


■. in 


Area in 


Area in 


Dia. in 


Cir 


. in 


Area in 


Area in 


ft. 


in. 


fl. 


in. 


SQ. inch. 


sq. ft. 


ft. 


in. 


ft. 


in. 


sq. inch. 


sq. ft. 


3 


2 


9 


11% 


1134.12 


7.8681 


4 


4 


13 


7% 


2123.72 


14.748 


3 


214 


10 


oys 


1149.09 


7.9791 


4 


414 


13 


8% 


2144.19 


14.890 


3 


2y. 


10 


oys 


1164.16 


8.0846 


4 


4^1 


13 


8ys 


2164.75 


15.033 


3 


2% 


10 


1% 


1179.32 


8.1891 


4 


4% 


13 


9% 


2185.42 


15.176 


3 


3 


10 


2y2 


1194.59 


8.2951 


4 


5 


13 


loy. 


2206.18 


15.320 


3 


'6Vi 


10 


3y4 


1209.95 


8.4026 


4 


514 


13 


iiy: 


2227.05 


15.465 


3 


31/3 


10 


4 


1225.42 


8.5091 


4 


5y2 


14 





2248.01 


15.611 


3 


3% 


10 


4% 


1240.98 


8.6171 


4 


5% 


14 


0% 


2269.06 


15.757 


3 


4 


10 


5% 


1256.64 


8.7269 


4 


6 


14 


1% 


2290.22 


15.904 


3 


434 


10 


6% 


1272.39 


8.8361 


4 


6V4 


14 




2311.48 


16.051 


3 


4y2 


10 


"iVi 


1288.25 


8.9462 


4 


6V2 


14 


31/ 


2332.83 


16.200 


3 


4% 


10 


8 


1304.20 


9.0561 


4 


6% 


14 


4 


2354.28 


16.349 


3 


5 


10 


8% 


1320.25 


9.1686 


4 


7 


14 


4% 


2375.83 


16.498 


3 


514 


10 


^¥1 


1336.40 


9.2112 


4 


7yL 


14 


5y2 


2397.48 


16.649 


3 


51/2 


10 


10% 


1352.65 


9.3936 


4 


7y2 


14 


6-7. 


2419.22 


16.800 




5% 


10 


iiy* 


1369.00 


9.5061 


4 


7% 


14 


7% 


2441.07 


16.951 


3 


6 


10 


11% 


1385.44 


9.6212 


4 


8 


14 


7% 


2463.01 


17.104 


3 


6% 


11 


0% 


1401.98 


9.7364 


4 


81^ 


14 


%-/. 


2485.05 


17.256 


3 


eyo 


11 


iy2 


1418.62 


9.8518 


4 


8y2 


14 


9y2 


2507.19 


17.411 


3 


6% 


11 


2y4 


1435.36 


9.9671 


4 


8% 


14 


ioy4 


2529.42 


17.565 


3 


7 


11 


3 


1452.20 


10.084 


4 


9 


14 


11 


2551.76 


17.720 


3 


7^4 


11 


3% 


1469.14 


10.202 


4 


^Vi 


14 


11% 


2574.19 


17.876 


3 


7y2 


11 


4% 


1486.17 


10.320 


4 


9y2 


15 


0^^ 


2596.72 


18.033 


3 


7% 


11 


5% 


1503.30 


10.439 


4 


9% 


15 


1% 


2619.35 


18.189 


3 


8 


11 


QVi 


1530.53 


10.559 


4 


10 


15 


2y4 


2642.08 


18.347 


3 


8y4 


11 


7 


1537.86 


10.679 


4 


3014 


15 


2ys 


2664.91 


18.506 


3 


8y2 


11 


7% 


1555.28 


10.800 


4 


loy. 


15 


3% 


2687.83 


18.665 


3 


8% 


11 


sy. 


1572.81 


10.922 


4 


10% 


15 


4i/> 


2710.85 


18.825 


3 


9 


11 


9% 


1590.43 


11.044 


4 


11 


15 


5yi 


2733.97 


18.965 


3 


»V4 


11 


loys 


1608.15 


11.167 


4 


11^4 


15 


evs 


2757.19 


19.147 


3 


9y, 


11 


10% 


1625.97 


11.291 


4 


iiy2 


15 


6% 


2780.51 


19.309 


3 


9% 


11 


11% 


1643.89 


11.415 


4 


11% 


15 


7% 


2803.92 


19.471 


3 


10 


12 


0V2 


1661.90 


11.534 


5 





15 


8y2 


2827.44 


19.635 




ioy4 


12 


ly^ 


1680.02 


11.666 


5 


014 


15 


914 


2851.05 


19.798 




loy. 


12 


2 


1698.23 


11.793 


5 


oy, 


15 


10 


2874.76 


19.963 




10% 


12 


2% 


1716.54 


11.920 


6 


0% 


15 


10% 


2898.56 


20.128 




n 


12 


3ys 


1734.94 


12.048 


5 


1 


15 


11% 


2922.47 


20.294 




1114 


12 


4% 


1753.45 


12.176 


5 


1% 


16 


0% 


2946.47 


20.461 




iiyo 


12 


5% 


1772.05 


12.305 


5 


]y2 


16 


1^/4 


2970.57 


20 629 




ii^t 


12 


6 


1790.76 


12.435 


5 


1% 


16 


1% 


2994.77 


20.797 







12 


6% 


1809.56 


12.566 


5 


2 


16 


2% 


3019.07 


20.965 




014 


12 


7y2 


1828.46 


12.697 


5 


2^ 
21/2 


16 


3l^ 


3043.47 


21.135 




0% 


12 


8% 


1847.45 


12.829 


5 


16 


414 


3067.96 


21.305 




0% 


12 


9y8 


1866.55 


12.962 


5 


2% 


16 


sys 


3092.56 


21.476 




1 


12 


9% 


1885.74 


13.095 


5 


3 


16 


5"/8 


3117.25 


21.647 




iy4 


12 


10% 


1905.03 


13.229 


5 


syL 


16 


6y4 


3142.04 


21.819 




■^14 


12 


iiy. 


1924.42 


13.304 


5 


3% 


16 


74 


3166.92 


21.992 




1% 


13 


oyl 


1943.91 


13.499 


5 


3% 


16 


8y4 


3191.91 


22.166 




2 


13 


1 


1963.50 


13.635 


5 


4 


16 


9 


3216.99 


22.333 




2y4 


13 


1% 


1983.18 


13.772 


5 


414 


16 


9% 


3242.17 


22.515 




2y2 


13 


2V, 


2002.96 


13.909 


5 


4i| 


16 


10% 


3267.46 


22.621 




oa^ 


13 


3% 


2022.84 


14.047 


5 


4% 


16 


11% 


3292.83 


22.866 




3 


13 


^ 4% 


2042.82 


14.186 


5 


5 


17 


oy* 


3318.31 


23.043 




^Y^ 


13 


5 


2062.90 


14.325 


5 


514 


17 


o-/« 


3343.88 


23.221 




IYj 


13 


5% 


2083.07 


14.465 


5 


5vt 


17 


1% 


3369 56 


23.330 




3% 


13 


6% 


2103.35 


14.606 


5 


5?4 


17 


2V2' 


3395.33 


23.578 



Tables, Rules and Recipes. 



Dia. in 


Cir 


. in 


Area in 


Area in 


Dia. in 


Cir 


. in 


Area in 


Area in 


ft. 


iu. 


ft. 


in. 


sq. inch. 


sq. ft. 


ft. 


in. 


ft. 


in. 


sq. incli. 


sq. ft. 


5 


6 


17 


3% 


3421.20 


23.758 


6 


4 


19 


10% 


4o36.47 


31.5O0 


5 


6^ 


17 


4ys 


3447.16 


23.938 


6 


41/4 


19 


11% 


4566.36 


31.710 


5 


cy2 


17 


4% 


3473.23 


24.119 


6 


4y2 


20 


0% 


4596.35 


31.919 


6 


6% 


17 


5% 


3499.39 


24.301 


6 


4% 


20 


1% 


4626.44 


32.114 


5 


7 


17 


61/2 


3525.26 


24.483 


6 


5 


20 


1% 


4656.63 


32.337 


5 


TU 


17 


71/4 


35.32.01 


24.666 


6 


51/4 


20 


2% 


4686.92 


32.548 


5 


7y2 


17 


8 


3578.47 


24.850 


6 


51/2 


20 


3% 


4717.30 


32.759 


5 


7% 


17 


8% 


3605.03 


25.034 


6 


5% 


20 


4% 


4747.79 


32.970 


5 


8 


17 


9% 


3631.68 


25.220 


G 


6 


20 


5 


4778.37 


33.183 


5 


81/4 


17 


10% 


3658.44 


25.405 


6 


61/4 


20 


5% 


4809.05 


33.396 


5 


8V2 


17 


11% 


3685.29 


25.592 


6 


61/2 


20 


61/2 


4839.83 


33.619 


5 


8% 


17 


11% 


3712.24 


25.779 


6 


6% 


20 


7% 


4870.70 


33.824 


5 


9 


18 


0% 


3739.28 


25.964 


6 


7 


20 


8% 


4901.68 


34.039 


5 


^Vi 


18 


iy2 


3766.43 


26.155 


6 


7y4 


20 


8% 


49.32.75 


34.255 


5 


Ol^ 


18 


2y; 


3793.67 


26.344 


6 


71/2 


20 


9% 


4963.92 


34.471 


5 


9% 


18 


3ys 


3821.02 


26.534 


6 


7% 


20 


10% 


4995.19 


34.688 


5 


10 


18 


3ys 


3848.46 


26.725 


6 


8 


20 


11% 


5026.26 


34.906 


5 


10!4 


18 


4% 


3875.99 


26.91«; 


6 


81/4 


21 


0% 


5058.02 


35.125 


5 


3 01/2 


18 


r3i/2 


3903.63 


27.108 


6 


81/2 


21 


0% 


5089.58 


35.344 


5 


10% 


18 


61/4 


3931.36 


27.301 


6 


8% 


21 


1% 


5121.24 


35.564 


5 


11 


18 


7 


3959.20 


27.494 


6 


9 


21 


2% 
3% 


5153.00 


35.784 


5 


111/4 


18 


7% 


3987.13 


27.688 


6 


014 


21 


5184.86 


36.006 


5 


11 1/2 


18 


8% 


4015.16 


27.883 


6 


91/2 


21 


4 


5216.82 


36.227 


5 


11% 


18 


9% 


4043.28 


28.078 


6 


9% 


21 


4% 


5248.87 


36.450 


6 





18 


lOi/s 


4071.51 


28.274 


6 


10 


21 


5% 


5281.02 


36.674 


6 


014 


18 


10% 


4099.83 


28.471 


6 


101/4 


21 


6% 


531S.27 


36.897 


6 


oy2 


18 


11% 


4128.25 


28.663 


6 


lOV, 


21 


7% 


5345.62 


37.12:> 


6 


0% 


19 


01/2 


4156.77 


28.866 


6 


10% 


21 


7% 


5378.07 


37.347 


6 


1 


19 


1^4 


4185.39 


29.064 


6 


11 


21 


8% 


5410.62 


37.573 


6 


1^4 


19 


2ys 


4214.11 


29.264 


6 


1114 


21 


9% 


5443.26 


37.700 


fi 


iy2 


19 


278 


4242.92 


29.466 


6 


11% 


21 


1014 


5476.00 


38.027 


6 


1% 


19 


3% 


4271.83 


29.665 


6 


11% 


21 


11 


5508.84 


38.256 








19 


41/j 


4300.85 


29.867 














6 


214 


19 


51/4 


4329.95 


30.069 














6 


21/2 


19 


G 


4359.16 


30.271 














6 


2% 


19 


G% 


4388.47 


30.475 














6 


3 


19 


7% 


4417.87 


30.619 














6 


3y4 


]9 


8% 


4447.37 


30.884 














Ci 


81/, 


19 


91/s 


4470.97 


31.090 














G 


3% 


19 


9% 


4500.67 


31.296 















Tables, Rules and Reel pes. 



103 



Dia 


. in 


Circum. in 




Dia 


. in 


Circum. in 




ft. 


in. 


ft. 


in. 


Area in feet. 


ft. 


in. 


ft. 


in. 


Area in feet. 


7 





21 


ll'/8 


38.4846 


11 





34 


6% 


95.0334 




1 


22 


3 


39.4060 


11 


1 


34 


9% 


96.4783 


7 


2 


92 


QVs 


40.3388 


11 


2 


35 


oys 


97.9347 


7 


3 


22 


914 


41.2825 


11 


3 


35 


li 


99.4021 


7 


4 


23 


0% 


42.2367 


11 


4 


35 


100.8797 


7 


5 


23 


21/8 


43.2022 


11 


5 


35 




102.3689 


7 


6 


23 


6% 


44.1787 


11 


6 


36 


1V2 


103.8601 


7 


7 


23 


11 


45.1656 


11 


7 


36 


4% 


105.3794 




8 


24 


IVs 


46.1638 


11 


8 


36 




106.9013 


7 


9 


24 


4^8 


47.1730 


11 


9 


36 


10% 


108.4342 


7 


10 


24 


714 


48.1926 


11 


10 


37 


2V^ 


109.9772 


7 


11 


24 


10% 


49.2236 


11 


11 


37 


5y4 


111.5319 


8 





25 


IV2 


50.2656 


12 





37 


8% 


113.0976 


8 


1 


25 


4% 


51.6178 


12 


1 


37 


iiya 


114.6732 


8 


2 


25 


7'/s 


52.3816 


12 


2 


38 


2% 


116.2607 


8 


3 


25 


11 


53.4562 


12 


3 


38 


5% 


117.8590 


S 


4 


26 


2y8 


54.5412 


12 


4 


38 


8y8 


119.4674 


8 


5 


26 


514 


55.6377 


12 


5 


39 





121.0876 


s 


6 


26 


8% 


56.7451 


12 


6 


39 


3y4 


122.7187 


8 


7 


26 


IIV3 


57.8628 


12 


7 


39 


6% 


124.3593 


8 


8 


27 


2% 


58.9920 


12 


8 


39 


oyo 


126.0127 


8 


9 


07 


5% 


60.1321 


12 


9 


40 


0% 


127.6765 


8 


30 


27 


9 


61.2826 


12 


10 


40 


3% 


129.3504 


8 


11 


28 


OVs 


62.4445 


12 


11 


40 


6ys 


131.0369 


9 





28 


314 


63.6174 


13 





40 


10 


132.7326 


9 


1 


28 


6% 


64.8006 


13 


1 


41 


1% 


134.4391 


9 


2 


28 


91/2 


65.9951 


13 


2 


41 


4% 


136.1574 


9 


3 


29 




67.2007 


13 


3 


41 


7y2 


137.8867 


9 


4 


29 


3% 


68.4166 


13 


4 


41 


10% 


139.6260 


9 


5 


29 


7 


69.6440 


13 


5 


42 


1% 


141.3771 


9 


6 


29 


lOVs 


70.8823 


13 


6 


42 


4y8 


143.1391 


9 


7 


30 


IV4 


72.1309 


13 


7 


42 


8 


144.9111 


9 


8 


30 


4% 


73.3910 


13 


8 


42 


iiys 


146.6949 


9 


9 


30 


71/2 


74.6620 


13 


9 


43 


2y+ 


148.4896 


9 


10 


30 


11% 


75.9433 


13 


10 


43 


5y2 


150.2943 


•> 


11 


31 


1% 


77.2362 


13 


11 


43 


8% 


152.1109 


10 





31 


5 


78.5400 


14 





43 


11% 


153.9484 


10 


1 


31 


8V8 


79.8540 


14 


1 


44 


2-| 


155.7758 


10 


2 


31 


IIV4 


81.1795 


14 


9 


44 


6 


157.6250 


10 


3 


32 


2% 


82.5190 


14 


3 


44 


91/8 


159.4852 


10 


4 


32 


51/2 


83.8627 


14 


4 


45 


Oi/t 


161.3553 


10 


5 


32 


8% 


85.2211 


14 


5 


45 


3y2 


163.2373 


10 


6 


32 


31% 


86.5903 


14 


6 


45 


6% 


165.1303 


10 


7 


33 


2% 


87.9697 


14 


7 


45 


9% 


167.0331 


10 


8 


33 


61/8 


80.3668 


14 


8 


46 


oys 


168.9479 


10 


9 


33 


9Vi 


90.7627 


14 


9 


46 


4 


170.8735 


10 


10 


34 


0% 


92.1749 


14 


10 


46 


7y8 


172.8091 


10 


11 


34 


31/2 


93.5986 


14 


11 


46 


iiy4 


174.7565 



104 



Tables, Rules and Recipes. 



Dia 


. in 


Circum. in 




Dia 


in 


Circum. in 




ft. 


in. 


ft. 


in. 


Area in feet. 




in. 


ft. 


in. 


Area in feet. 


15 





47 


iy2 


176.7150 







53 


4ys 


226.9806 


15 


1 


47 


4% 


178.68^2 




1 


53 


8 


229.2105 


15 


2 


47 


7'| 


180.6624 




2 


53 


llVs 


231.4625 


15 


3 


47 


10% 


182.6545 




3 


54 


21/8 


233.7055 


15 


4 


48 


2V2 


184.6555 




4 


54 


5% 


235.9682 


15 


5 


48 


SVs 


186.6684 




5 


54 


81/2 


238.2430 


15 


6 


48 


81/4 


188.6923 




6 


54 


11% 


240.5287 


15 


7 


48 


11% 


190.7260 




7 


55 


2% 


242.8241 


15 


8 


49 


2% 


192.7716 




8 


55 


6 


245.1316 


15 


9 


49 


5% 


194.8282 




9 


55 


91/8 


247.4500 


15 


10 


49 


8% 


196.8946 




10 


56 


01/4 


249.7781 


15 


11 


50 





198.9730 




11 


56 


31/2 


252.1184 


16 





50 


SVg 


201.0624 


18 





56 


eva 


254.4696 


16 


1 


50 


6% 


203.1615 


18 


1 


56 


9% 


256.8303 


16 


2 


50 


9% 


205.2726 


18 


2 


57 


078 


259.2033 


16 


3 


51 


01/2 


207.3946 


18 


3 


57 


4 


261.5872 


16 


4 


51 


3% 


209.5264 


18 


4 


57 


7% 


263.9807 


16 


5 


51 


61/2 


211.6703 


18 


5 


57 


101/4 


266.3864 


16 


6 


51 


10 


213.8251 


18 


6 


58 


1% 


268.8031 


16 


7 


52 


1V8 


215.9896 


18 


7 


58 


41/2 


271.2293 


16 


8 


• 52 


41/4 


218.1662 


18 


8 


58 


7% 


273.6678 


16 


9 


52 


7% 


220.3537 


18 


9 


58 


10% 


276.1171 


16 


10 


52 


101/2 


222.5510 


18 


10 


59 


2 


278.5761 


16 


11 


53 


1% 


224.7603 


18 


11 


59 


5y2 


281.0472 



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;-J 1-1 C<1 " CO ' ' ■* CM 

Usn OP THE Tablr : To find the capacity of any cylindrical measure, 
from 1 inch diameter to 30 inches, take the inside diameter of the meas- 
ure in inches, and multiply the area in the table which corresponds to 
the diameter by the depth in inches, and divide the products, if gills 
are required, by 7.2135 • if pints, by 2S.875 ; if quarts, by 57.75 : and if gal- 
lons, by 231. If bushels are required (say in a tierce or barrel, after the 
mean diameter is obtained), multiply as above, and divide the product 
by 215U.42 ; the quotient is the number of bushels. Calling the diameters 
feet the areas are feet, — then, if a ship's water tank, steam boiler, etc., 
is 5^s. or any number of feet and parts of feet in diameter, find the 
area in the table which corresponds in inches, multiply it by the length 
in feet, and multiply this result bv the number of gallons in a cubic 
foot (7.4805). and the product is the answer in gallons. In any case 
where there are more figures in the divisor than in the dividend, add 
ciphers. 



> Tables, Rules and Recipes. 

CAPACITY OF CANS ONE INCH DEEP. 



USE OF THE TABLE. 



Required the contents of a vessel, diameter 6 7-10 inches, depth 10 
inches. 

By the table a vessel 1 inch deep and 6 7-10 inches diameter contains 
.15 (hundredths) gallon, then 15 X 10 — 1.50, or 1 gallon and 2 quarts. 

Required the contents of a can, diameter 19 8-10 inches, depth 30 
inches. 

By the table a vessel 1 inch deep and 19 8-10 inches diameter con- 
tains 1 gallon and .33 (hundredths), then 1.33 X 30 = 39.90, or nearly 40 
gallons. 

Required the depth of a can whose diameter is 12 2-10 inches, to 
contain 16 gallons. 

By the table a vessel 1 inch deep and 12 2-10 inches diameter contains 
.50 (hundredths) gallon, then 16 -^ .50 = 32 inches, the depth required. 



Diam 






















eter 




^ /lO 


Vio 


Vio 


Vio 


•■^/lo 


Vio 


Vio 


Vio 


Vio 


3 


.03 


.03 


.03 


.03 


.03 


.04 


.04 


.04 


.04 


.05 


4 


.05 


.05 


.05 


.05 


.06 


.06 


.07 


.07 


.07 


.08 


5 


.08 


.08 


.08 


.08 


.09 


.10 


.10 


.11 


.11 


.11 


6 


.12 


.12 


.12 


.13 


.13 


.14 


.14 


.15 


.15 


.16 


7 


.16 


.17 


.17 


.18 


.18 


.19 


.19 


.20 


.20 


.21 


8 


.21 


.22 


.22 


.23 


.23 


.24 


.25 


.25 


.26 


.26 


9 


.27 


.28 


.28 


.29 


.30 


.30 


.31 


.31 


.32 


.33 


10 


.34 


.34 


.35 


.36 


.36 


.37 


.38 


.38 


.39 


.40 


11 


.41 


.41 


.42 


.43 


.44 


.44 


.45 


.46 


.47 


.48 


12 


.48 


.49 


.50 


.51 


.52 


.53 


..53 


.54 


.55 


.56 


13 


.57 


.58 


.59 


.60 


.60 


.61 


.62 


.63 


.64 


.65 


14 


.66 


.67 


.68 


.69 


.70 


.71 


72 


.73 


.74 


.75 


15 


.76 


.77 


.78 


.79 


.80 


.81 


'.fi 


.83 


.84 


.85 


16 


.87 


.88 


.89 


.90 


.91 


.92 


.93 


.94 


.95 


.97 


17 


.98 


.99 


1.005 


1.017 


1.028 


1.040 


1.051 


1.063 


1.075 


1.086 


18 


1.101 


1.113 


1.125 


l.K^S 


1.150 


1.162 


1.170 


1.187 


1.200 


1.211 


19 


1.227 


1.240 


1.253 


1.266 


1.279 


1.292 


1.304 


1.317 


1.330 


1.343 


20 


1.360 


1.373 


1.385 


1.400 


1.414 


1.428 


1.441 


1.455 


1.478 


1.482 


21 


1.499 


1.513 


1.527 


1.542 


1.556 


1.570 


1.585 


1.600 


1.612 


1.630 


22 


1.645 


1.660 


1.675 


1.696 


1.705 


1.720 


1.735 


1.750 


1.770 


1.780 


23 


1.798 


1.814 


1.830 


1.845 


1.861 


1.876 


1.892 


1.908 


1.923 


1.940 


24 


1.958 


1.974 


1.991 


2.007 


2.023 


2.040 


2.056 


2.072 


2.096 


2.105 


25 


2.125 


2.142 


2.159 


2.176 


2.193 


2.120 


2.227 


2.244 


2.261 


2.280 


26 


2.298 


2.316 


2.333 


2.351 


2.369 


2.386 


2.404 


2.422 


2.440 


•2.460 


27 


2.478 


2.496 


2.515 


2.533 


2.552 


2.570 


2.588 


2.607 


2.625 


2.643 


28 


2.665 


2.684 


2.703 


2.722 


2.741 


2.764 


2.780 


2.800 


2.820 


2.836 


29 


2.859 


2.879 


2.898 


2.918 


2.938 


2.958 


2.977 


2.997 


3.017 


3.036 


30 


3.060 


3.080 


3.100 


3.121 


3.141 


3.162 


3.182 


3.202 


3.223 


3.245 


31 


3.267 


3.288 


3.309 


3.330 


3.351 


3.372 


3.393 


3.414 


3.436 


3.457 


32 


3.481 


3.503 


3.524 


3.543 


3.568 


3.590 


3.612 


3.633 


3.655 


3.589 


33 


3.702 


3.725 


3.747 


3.773 


3.795 


3.814 


3.8.37 


3.860 


3.882 


3.904 


34 


3.930 


3.953 


3.976 


4.003 


4.022 


4.046 


4.070 


4.092 


4.115 


4.140 


35 


4.165 


4.188 


4.212 


4.236 


4.260 


4.284 


4.307 


4.331 


4.355 


4.380 


36 


4.406 


4.430 


4.455 


4.483 


4.503 


4.528 


4.553 


4.577 


4.602 


4.626 


37 


4.654 


4.679 


4.704 


4.730 


4.755 


4.780 


4.805 


4.834 


4.855 


4.880 


38 


4.909 


4.935 


4.961 


4.987 


5.012 


5.038 


6.064 


5.090 


5.120 


5.142 


39 


5.171 


5.197 


5.224 


5.250 


5.277 


5.304 


5.330 


5.357 


5.383 


5.410 


40 


5.440 


5.467 


5.491 


5.521 


5.548 


5.576 


5.603 


5.630 


5.657 


5.684 



Tables, Rules and Recipes. lOy 

RULES FOR CALCULATING CIRCUM- 
FERENCES. 

1st. Multiply the given diameter by 22, and divide the 
product by 7 ; or 2d, divide 22 by 7 and multiply the di- 
ameter by the quotient; or 3d, multiply the diameter by 
3.1416; or 4th, multiply the diameter by 3 and add i inch 
for every 7 of the diameter, or about yi inch for every i. 
For example: If the given diameter be 15 inches, by the 
first rule the circumference would be 47 1-7 inches ; by the- 
second, 47 1-7 inches ; by the third, 47.1240 inches ; by the 
fourth, 47 >^ inches ; by the table, 47 >^ inches. It will be 
seen that the result is not just the same by the several 
rules, yet either is near enough for general use and prac- 
tice. 

WEIGHT OF WATER. 

1 cubic inch is equal to .03617 pouud. 

12 cubic inches is equal to .434 pound. 

1 cubic foot IS equal to G2.5 pounds. 

1 cubic foot is e(iual to T.5U U.S. gallons. 

1.8 cubic feet is equal to 1V2.00 pounds. 

35.84 cubic feet is equal to 2240.00 pounds. 

1 cylindrical inch is equal to .02842 pound. 

12 cj^lindrical inches is equal to .341 pound. 

1 cylindrical foot is equal to 40.10 pounds. 

1 cylindrical foot is equ.i! to (i.OO U. S. gallo 1^. 

2,282 cylindrical feet is equal to 112.00 pounds. 

45.G4 cylindrical feet is equal to 2240.00 pounds. 

13.43 United States gallons. . .is equal to 112.00 pounds. 

268.8 United States gallons. . .is equal to 2240.00 pounds. 

Center of pressure is at two-thirds depth from surface. 

TO FIND NUMBER OF BARRELS IN 
CISTERNS. 

The following table shows the number of barrels (31^ 
gallons) contained in cisterns of various diameters, from 
5 to 30 feet, and of depths ranging from 5 to 20 feet. 



o8 



Tables, Rules and Recipes. 



To use the table, find the required depth in the side 
cokimn, and then follow along the line to the column 
which has the required diameter at the top. Thus, with 
a cistern 6 feet deep and i6 feet in diameter, we find 6 
in the second line, and then follow along until column i6 
is reached, when we find that the contents is 286.5 barrels. 

NUMBER OF BARRELS (3I>4 GALLONS) IN CISTERNS AND 

TANKS. 



Diameter in feet. 



Depth in 
feet. 5 


6 


7 


8 


9 


10 


11 


12 


13 


5 


23.3 


33.6 


45.7 


59.7 


75.5 


93.2 


112.8 


134.3 


157.6 


6 


28.0 


40.3 


54.8 


71.7 


90.6 


111.9 


135.4 


161.1 


189.1 


7 


32.7 


47.0 


64.0 


83.6 


105.7 


130.6 


158.0 


188.0 


220.6 


8 


37.3 


53.7 


73.1 


95.5 


120.9 


149.2 


180.5 


214.8 


252.1 


9 


42.0 


60.4 


82.2 


107.4 


136.0 


167.9 


203.1 


241.7 


283.7 


10 


46.7 


67.1 


91.4 


119.4 


151.1 


186.5 


225.7 


268.6 


315.2 


11 


51.3 


73.9 


100.5 


131.3 


166.2 


205.1 


248.2 


295.4 


346.7 


12 


56.0 


80.6 


109.7 


143.2 


181.3 


223.8 


270.8 


322.3 


378.2 


13 


60.7 


87.3 


118.8 


155.2 


196.4 


242.4 


293.4 


349.1 


409.7 


14 


65.3 


94.0 


127.9 


167.1 


2n.5 


261.1 


315.9 


376.0 


441.3 


15 


70.0 


100.7 


137.1 


179.0 


226.6 


289.8 


338.5 


402.8 


472.8 


16 


74.7 


107.4 


146.2 


191.0 


241.7 


298.4 


361.1 


429.7 


504.3 


17 


79.3 


114.1 


155.4 


202.9 


256.8 


317.0 


383.6 


456.6 


535.8 


18 


84.0 


120.9 


164.5 


214.8 


272.0 


335.7 


406.2 


483.4 


567.3 


19 


88.7 


127.6 


173.6 


226.8 


287.0 


354.3 


428.8 


510.3 


598.0 


20 


93.3 


134.3 


182.8 


238.7 


302.1 


373.0 


451.3 


537.1 


630.4 










Diameter in feet. 








Depth in 


















feet 


:. 14 


15 


16 


17 


18 


19 


20 


21 


22 


5 


182.8 


209.8 


238.7 


269.5 


302.1 


336.6 


373.0 


411.2 


451.3 


6 


219.3 


251.8 


286.5 


323.4 


362.6 


404.0 


447.6 


493.5 


541.6 


7 


255.9 


293,7 


334.2 


377.3 


423.0 


471.3 


522.2 


575.7 


631.9 


8 


292.4 


335.7 


382.0 


431.2 


483.4 


538.6 


596.8 


658.0 


722.1 


9 


329.0 


377.7 


429.7 


485.1 


543.8 


605.9 


671.4 


740.2 


812.4 


10 


365.5 


419.6 


477.4 


539.0 


604.3 


673.3 


746.0 


822.5 


902.7 


11 


402.1 


461.6 


525.2 


592.9 


667.7 


740.6 


820.6 


904.7 


992.9 


12 


438.6 


503.5 


572.9 


646.8 


725.1 


807.9 


895.2 


987.0 


1083.2 


13 


475.2 


545.5 


620.7 


700.7 


785.5 


875.2 


969.8 


1069.2 


1173.5 


14 


511.8 


587.5 


668.2 


754.6 


846.6 


942.6 


1044.4 


1151.5 


1263.7 


15 


548.3 


629.4 


716.2 


308.5 


906.0 


3009.9 


1119.0 


1233.7 


1354.0 


16 


584.9 


671.4 


773.9 


862.4 


966.8 


1077.2 


1193.6 


1315.9 


1444.3 


17 


621.4 


713.4 


811.6 


916.3 


3027.2 


1144.6 


1268.2 


1398.2 


1534.5 


IS 


658.0 


755.3 


859.4 


970.2 


1087.7 


1211.9 


1342.8 


1480.4 


1624.8 


19 


694.5 


797.3 


907.1 


1024.1 


1148.1 


1279.2 


1417.4 


1562.7 


1715.1 


20 


731.1 


839.3 


954.9 


1078.0 


1208.5 


1346.5 


1492.0 


1644.9 


1805.3 



Tables, Rules and Recipes. 



109 



Diameter in feet. 



Dept 
feet 


hin 
23 


24 


25 


26 


27 


28 


29 


30 


5 


493.3 


537.1 


582.8 


630.4 


679.8 


731.1 


784.2 


839.3 


6 


592.0 


644.5 


699.4 


756.5 


815.8 


877.3 


941.1 


1007.1 


7 


690.6 


752.0 


815.9 


882.5 


951.7 


1023.5 


1097.9 


1175.0 


8 


789.3 


859.4 


932.5 


1008.6 


1087.7 


1169.7 


1254.8 


1342.8 


9 


887.9 


966.8 


1049.1 


1134.7 


1223.6 


1316.0 


1411.6 


1510.7 


10 


986.6 


1074.2 


1165.6 


1260.8 


1359.6 


1462.2 


1568.2 


1678.5 


11 


1085.2 


1181.7 


1282.2 


1386.8 


1495.6 


1608.7 


1723.0 


1846.4 


12 


1183.9 


1289.1 


lo98.7 


1512.9 


1631.5 


1754.6 


1882.2 


2014.2 


13 


1282.6 


1396.5 


1515.3 


1639.0 


1767.5 


1900.8 


2039.0 


2182.0 


It 


1381.2 


1503.9 


1631.9 


1765.1 


1903.4 


2047.1 


2195.9 


2343.9 


15 


1479.9 


1611.4 


1748.4 


1891.1 


2039.4 


2193.3 


2352.7 


2517.8 


n; 


1578.5 


1718.8 


1865.0 


2017.2 


2175.4 


2339.5 


2509.6 


2685.6 


17 


1677.2 


1826.2 


1981.6 


2143.3 


2311.3 


2485.7 


2966.4 


2853.5 


18 


1775.9 


1933.6 


2098.1 


2269.4 


2447.3 


2631.9 


2823.3 


3021.3 


19 


1874.5 


2041.1 


2214.7 


2395.4 


2583.2 


2778.1 


2980.1 


3189.2 


20 


1973.2 


2148.5 


2321.2 


2521.5 


2U9.2 


2924.4 


3137.0 


3357.0 



For tanks that are tapering tlie diameter may be measured four- 
tc-nths from large end. 

TABLE SHOWING THE PRESSURE OF W.\TER PER SQUARE 
INCH, DUE TO DIFFERENT HEADS, FROM I TO 25O FEET. 



Head. 


Pressure in lbs. 


Head. 


Pressure in lbs. 


Head. 


Pressure in 1 


1 


.4335 


J9 


8.237 


37 


16.04 


2 


.8670 


20 


8.670 


38 


16.47 


3 


1.300 


21 


9. J 04 


39 


16.91 


4 


1.734 


22 


9.537 


40 


17.34 


5 


2.167 


23 


9.971 


50 


21.67 


6 


2.601 


24 


10.40 


100 


43.35 


7 


3.035 


25 


10.84 


110 


47.68 


8 


3.408 


26 


11.27 


120 


52.02 


9 


3.902 


27 


11.70 


130 


56.36 


10 


4.335 


28 


12.14 


140 


60.69 


11 


4.768 


29 


12.57 


150 


65.03 


12 


5.202 


30 


13.00 


160 


69.36 


13 


5.636 


31 


13.44 


170 


73.70 


14 


6.069 


22 


13.87 


180 


78.03 


15 


6.503 


33 


14.31 


190 


82.36 


16 


6.936 


34 


14.74 


200 


86.70 


17 


7.370 


35 


15.17 


225 


97.41 


18 


7.803 


36 


15.60 


250 


108.37 



MEASURES OF CAPACITY AND WEIGHT. 

. Measures of Weight. — Avoirdupois. — 16 drams 
equal i ounce; 1 6 ounces i pound; 112 pounds i hundred- 
weight ; 20 hundredweights i ton. Troy. — 24 grains i 
pennyweight; 20 pennyweights i ounce; 12 ounces i 
pound. Apothecaries'. — 20 grains equal i scruple ; 3 
scruples i dram; 8 drams i ounce; 12 ounces i pound. 



no Tables, Rules and Recipes. 

Measures of Capacity (Dry). — 2150.42 cubic inches 
equal i United States (or Winchester) bushel; the di- 
mensions of which are i8>4 inches diameter inside, 19^^ 
inches outside and 8 inches deep; 2747.70 cubic inches 
equal i heaped bushel, the cone of which must not be less 
than 6 inches high. 

Measures of Capacity (Liquids). — 231 cubic inches 
equal i United States standard gallon ; 277.274 cubic 
inches equal i Imperial (British) gallon; 31^ United 
States gallons equal i barrel ; 42 gallons equal i tierce ; 
63 gallons equal i hogshead ; 84 gallons equal i puncheon ; 
126 gallons equal i pipe ; 252 gallons equal i tun. 

French Measures of Frequent Reference^ Com- 
pared WITH U. S. Measures. — Meter, 3.28 feet; Deci- 
meter (i-io meter), 3.94 inches; Centimeter, .4 inch; 
Millimeter, .04 inch; Hectoliter, 26.42 gallons; Liter, 2. 11 
pints ; Kilogram, 2.2 pounds. 

Weights of Various Substances. — Pounds Avoir- 
dupois. — I cubic foot of bricks weighs 124 pounds; i do. 
of sand or loose earth, 95 ; i do. of cork, 15 ; i do. of gran- 
ite, 170; I do. of cast iron, 450; i do. of wrought iron, 
485; I do. of steel, 490; i do. of copper, 555; i do. lead, 
709; I do. brass, 520; i do. tin, 459; i do. white pine, 30; 
I do. oak, 48 ; i do. sea water, 64.08 ; i do. fresh, 62.35 ; 
I do. air, 0765, 



Tables, Rules and Recipes. 



1 II 



SIZES OF TIN WARE IN THE FORM OF FRUS- 
TUM OF A CONE. 



PANS. 



Size. 
20 qt. 
16 " 
14 " 
10 " 
6 '• 


Diam. 

of top. 
191/, in. 
18 " " 
151/4 " 
14% '• 
12% " 


Diam. 

of bot. 
13 in. 
IIV4 •' 

91/4 " 
11 " 

9 " 


Hight. Size. 
8 in. 2 qt. 
614 " 3pt. 
61/4 " 1 " 
41/8 " Pie 


Diam. 
of top. 
9 in. 

81/4 " 

7^ ;; 


Diam. 
of bot. 
6 in. 


Hight. 
3% in. 






DISH 


KETTLES AND PAILS. 






Size. 
14 qt. 
10 " 


Diam. 
of top. 
13 in. 
llMs " 


Diam. 

of bot. 

9 in. 

7 " 


Ilight. Size. 
9 in. 6 qt. 

8 " 2 " 

COFFEE POTS. 


Diam. 
of top. 
914 in. 


Diam. 
of bot. 
51/2 in. 
4 " 


Hight. 
61/2 in. 
4 '• 


Size. 
Igal. 


Diam. 

of top. 
4 in. 


Diam. 

of bot. 
7 in. 


Ilight. Size. 
81/2 in. 3 qt. 

WASH BOWLS. 


Diam. 
of top. 
31/2 in. 


Diam. 
of bot. 
6 in. 


Hight. 
81/2 in. 


Size 
Large wash bowl 

Cullender 

Small wash bowl 
Milk strainer. . . 




••••••••• • 


Diam. 

of top. 
. 11 in. 
. 11 " 
. 91/2 " 
. 91/2 •' 


Diam. 

of bot. 
5% in. 

5% " 
51/2 " 


Hight. 
5 in. 
5 '• 

3% '• 
3% " 








DIPPERS. 








Size. 
V2 gal. 


Diam. 

of top. 

6M, in. 


Diam. 

of bot. 

4 in. 


Ilight. Size. 
4 in. 1 pt. 

MEASURES. 


Diam. 
of top. 

4y4 in. 


Diam. 
of bot. 
3% in. 


Hight. 

2% in. 


Size. 

1 gal 


Diam. 

of top. 

1. '5i/> in. 
4 " 
31/2 " 


Diam. 

of bot. 

ei/s in. 
4-/8 " 
4 " 


night. Size. 
914 in. 1 pt. 

8 " 1/0 " 
5% " 


Diam. 
of top. 

21/s in. 

2% " 


Diam. 
of bot. 
3% in. 

2% " 


Hight. 

41/4 in. 
31/8 " 




druggists' AND LIQUOR DEALERS' MEASURES 




Size. 
5 gal. 

3 |] 

1 '* 


Diam. 
of top. 
8 in. 
7 " 
6 " 
3% " 


Diam. 

of bot. 
131/2 in. 
111/2 " 

It " 


Hight. Size. 
12% in. 1/2 gal. 
10% " 1 qt. 
8% " 1 pt. 

71/3 " 1/2 •' 


Diam. 

of top. 

3y^ in. 

1% " 


Diam. 
of bot. 
6% in. 

r« :: 
3% " 


Hight. 
6 in. 

f^ :: 



112 Tables, Rules and Recipes. 

TABLE OF EFFECTS UPON BODIES BY HEAT. 

Degrees F. 

Cast iron thoroughly melts at 2,228 

Gold melts at 1.91^' 

Silver melts at 1. '^ 

Copper mel ts at 1.929 

Brass melts at 1,873 

Zinc melts at ^9 

Lead melts at 618 

Bismuth melts at 506 

Tin melts at 444 

Tin and lead, equal parts, melt at 418 

Tin 2 parts, bismuth 5 and lead 3, melt ai 199 



PRACTICAL RECEIPTS. 

SOLDERS. 

SOLDER FOR GOLD. 

Gold, 6 pennyweights ; silver, i pennyweight ; copper, 
2 pennyweights. ' 

SOLDER FOR SILVER, FOR THE USE OF JEWELERS. 

Fine silver, 19 pennyweights; copper, i pennyweight; 
sheet brass, to pennyweights. 

WHITE SOLDER FOR SILVER. 

Silver, i ounce ; tin, i ounce. 

WHITE SOLDER FOR RAISED BRITANNIA WARE. 

•Tin, 100 pounds ; copper, 3 ounces ; to make it free, 
,add lead, 3 ounces. 

BEST SOFT SOLDER FOR CAST BRITANNIA WARE. 

Tin, 8 pounds ; lead, 5 pounds. 

YELLOW SOLDER FOR BRASS OR COPPER. 

Copper, I pound ; zinc, i pound. 



Tables, Rules and Recipes. 113 

YELLOW SOLDER FOR BRASS OR COPPER. 

(Stronger than the last.) Copper, 32 pounds; zmc, 
29 pounds ; tin, i pound. 

SOLDER FOR COPPER. 

Copper, 10 pounds ; zinc, 9 pounds. 

BLACK SOLDER. 

Copper, 2 pounds ; zinc, 3 pounds ; tin, 2 ounces. 

BLACK SOLDER. 

Sheet brass, 20 pounds ; tin, 6 pounds ; zinc, i pound. 

SILVER SOLDER FOR PLATED METAL. 

Fine silver, 1 ounce ; brass, 10 pennyweights. 

plumbers' solder. 
Lead, 2 ; tin, i part. 

tinmen's solder-. 
Lead, i ; tin, i part. 

PEWTERERS' SOLDER. 

Tin, 2 ; lead, i part. 

HARD SOLDER. 

Copper, 2 ; zinc, i part. 

SOLDER FOR STEEL JOINTS. 

Silver, 19 pennyweights; copper, i pennyweight; 
brass, 2 pennyweights. Melt under a coat of charcoal 
dust. 

SOFT GOLD SOLDER 

Is composed of 4 parts gold, i of silver and i of copper. 
It can be made softer by adding brass, but the solder be- 
comes more liable to oxidize, 



114 



Tables, Rules and Recipes. 



CEMENT FOR MENDING EARTHEN AND GLASS WARE. 

I. Heat the article to be mended a little above boiling 
water heat, then apply a thin coating of gum shellac on 
both surfaces of the broken vessel, and when cold it will 
be as strong as it was originally. 2. Dissolve gum shellac 
in alcohol, apply the solution and bind the parts firmly 
together until the cement is perfectly dry. 

CEMENT FOR STONE WARE. 

Another cement in which an analogous substance, the 
curd of milk, is employed, is made by boiling slices of 
skim milk cheese into a gluey consistence in a great quan- 
tity of water, and then incorporating it with quicklime 
on a slab with a muller, or in a marble mortar. When 
this compound is applied warm to broken edges of stone 
ware, it unites them very firmly after it is cold. 

IRON RUST CEMENT 

Is made from 50 to 100 parts of iron borings, pounded and 
sifted, mixed with i part of sal ammoniac, and when it is 
to be applied, moistened with as much water as will give 
it a pasty consistency. Another composition of the same 
kind is made by mixing 4 parts of fine borings or filings of 
iron, 2 parts of potters' clay and i part of pounded pot- 
sherds, and making them into a paste with salt and water. 

CEMENT FOR IRON TUBES, BOILERS, ETC. 

Finely powdered iron, 66 parts ; sal ammoniac, i part ; 
water, a sufficient quantity to form a paste. 

CEMENT FOR IVORY, MOTHER OF PEARL, ETC. 

Dissolve I part of isinglass and 2 of white glue in 30 
of water, strain and evaporate to 6 parts. Add 1-30 part 



Tables, Rules and Reel pes. 115 

of gum mastic, dissolve in ^1 part of alcohol and i part of 
white zinc. When required for use warm and shake up. 

CEMENT FOR HOLES IN CASTINGS. 

The best cement for this purpose is made by mixing 
I part of sulphur in powder, 2 parts of sal ammoniac and 
80 parts of clean powdered iron turnings. Sufficient 
water must be added to make it into a thick paste, wdiich 
should be pressed into the holes or seams which are to be 
filled up. The ingredients composing this cement should 
be kept separate and not mixed until required for use. It 
is to be applied cold, and the casting should not be used for 
two or three days afterward. 

CEMENT FOR COPPERSMITHS AND ENGINEERS, 

Boiled linseed oil and red lead mixed together into a 
putty is often used by coppersmiths and engineers to se- 
cure joints. The washers of leather or cloth are smeared 
with this mixture in a pasty state. 

A CHEAP CEMENT. 

Melted brimstone, either alone or mixed with rosin 
and brick dust, forms a tolerably good and very cheap 
cement. 

plumbers' CEMENT 

Consists of black rosin, i part ; brick dust, 2 parts ; well 
incorporated by a melting heat. 

CEMENT FOR BOTTLE CORKS. 

The bituminous or black cement for bottle corks con- 
sists of pitch hardened by the addition of rosin and brick 
dust. 



ii6 Tables, Rules and Recipes. 

CHINA CEMENT. 

Take the curd of milk, dried and powdered, lo ounces ; 
quicklime, i ounce; camphor, 2 drams. Mix and keep in 
closely stopped bottles. When used, a portion is to be 
mixed with a little water into a paste, to be applied quickly. 

CEMENT FOR LEATHER. 

A mixture of India rubber and shellac varnish makes 
a very adhesive leather cement. A strong solution of 
common isinglass, with a little diluted alcohol added to 
it, makes an excellent cement for leather. 

MARBLE CEMENT. 

Take plaster of paris and soak it in a saturated solu- 
tion of alum, then bake the two in an oven, the same as 
gypsum is baked to make it plaster of paris ; after which 
they are ground to powder. It is then used as wanted, 
being mixed up with water like plaster and applied. It 
sets into a very hard composition capable of taking a very 
high polish. It may be mixed with various coloring min- 
erals to produce a cement of any color capable of imitating 
marble. 

CEMENT FOR MARBLE WORKERS AND COPPERSMITHS, 

White of an &gg alone, or mixed with finely sifted 
quicklime, will answer for uniting objects which are not 
exposed to moisture. The latter combination is very 
strong and is much employed for joining pieces of spar 
and marble ornaments. A similar composition is used by 
coppersmiths to secure the edges and rivets of boilers, only 
bullock's blood is the albuminous matter used instead of 
white of Q.gg, 



Tables, Rnlcs and Recipes. 117 

TRANSPARENT CEMENT FOR GLASS. 

Dissolve I part of iiidia rubber in 64 of chloroform, 
then add gum mastic in powder 14 to 24 parts, and digest 
for two days with frequent shaking. Apply with camel's 
hair brush. 

CEMENT TO MEND IRON POTS AND PANS. 

. Take 2 parts of sulphur, and i part, by weight, of fin^ 
black lead ; put the sulphur in an old iron pan, holding it 
over the fire until it begins to melt, then add the lead, stir 
well until all is mixed and melted, then pour out on an 
iron plate or smooth stone. When cool, break into small 
pieces. A sufficient quantity of this compound being 
placed upon the crack of the iron pot to be mended, cail 
be soldered by a hot iron in the same way a tinsmith 
solders his sheets. If there is a small hole in the pot, drive 
a copper rivet in it and then solder over it with this ce- 
ment. 

CEMENT TO RENDER CISTERNS AND CASKS WATER TIGHT. 

An excellent cement for resisting moisture is made by 
incorporating thoroughly 8 parts of melted glue, of the 
consistence used by carpenters, with 4 parts of linseed oil, 
boiled into varnish with litharge. This cement hardens 
in about 48 hours and renders the joints of wooden cis- 
terns and casks air and water tight. A compound of 
glue with one-quarter its weight of \>nice turpentine, 
made as above, serves to cement glass, metal and wood to 
one another. Fresh made cheese curd and old skim milk 
cheese, boiled in water to a slimy consistency, dissolved" in 
a solution of bicarbonate of potash are said to form a 
good cement for glass and porcelain. The gluten of 



11^ Tables, Rules and Recipes. 

wheat, well prepared, is also a good cement. White of 
cees with flour and water, well mixed, and smeared over 
linen cloth, forms a ready lute for steam joints in small 
apparatus. 

A GOOD CEMENT. 

Shellac, dissolved in alcohol or in a solution of borax, 
forms a pretty good cement. 

CEMENT FOR REPAIRING FRACTURED BODIES OF ALL KINDS. 

White lead ground upon a slab with linseed oil varnish 
and kept out of contact of air affords a cement capable 
of repairing fractured bodies of all kinds. It requires a 
few weeks to harden. When stone and iron are to be ce- 
mented together, a compound of equal parts of sulphur 
with pitch answers very well. 

CEMENT FOR CRACKS IN WOOD. 

Make a paste of slaked lime i part, rye meal 2 parts, 
vvith a sufficient quantity of linseed oil. Or dissolve i 
part of glue in 16 parts of water, when almost cool stir in 
sawdust and prepared chalk a sufficient quantity. Or 
oil varnish thickened with a mixture of equal parts of 
white lead, red lead, litharge and chalk. 

CEMENT FOR JOINING METALS AND WOOD. 

Melt rosin and stir in calcined plaster until reduced- to 
a paste, to which add boiled oil a sufficient quantity to 
bring it to the consistence of honey ; apply warm. Or, 
melt rosin 180 parts and stir in burnt umber 30, calcined 
plaster 15 and boiled oil 8 parts. 

GAS fitters' CEMENT. 

Mix together resin 4^^ parts, wax i part, and Venetian 
red 3 parts. 



Tables, Rules and Recipes. 119 

IMPERVIOUS CEMENT FOR APPARATUS, CORKS, ETC. 

Zinc white rubbed up with copal varnish to fill up the 
indentures ; When dry, to be covered with the same mass 
somewhat thinner, and lastly with copal varnish alone. 

CEMENT FOR FASTENING BRASS TO GLASS VESSELS. 

Melt rosin 150 parts, wax 30, and add burnt ocher 30 
and calcined plaster 2 parts. Apply warm. 

CEMENT FOR FASTENING BLADES, FILES, ETC. 

Shellac 2 parts, prepared chalk i, powdered and mixed. 
The opening for the blade is filled with this powder, the 
lower end of the iron heated and pressed in. 

HYDRAULIC CEMENT PAINT. 

If hydraulic cement be mixed with oil, it forms a first 
rate anti-combustible and excellent water proof paint for 
roofs of buildings, outhouses, walls, &c. 

TO STOP A LEAKY ROOF. 

Twenty-five pounds yellow ocher, i pound litharge, 
6 pounds black lead, i pound fine salt; boil well in oil. 
Soak strips of cloth in the above and paste over the seams. 
Good where solder is not practicable. 

FLUX FOR SOLDERING TIN ROOF. 

One part rosin and 2 parts binnacle oil mixed hot and 
used the same as rosin alone; -or, cut with alcohol i pint 
as much rosin as possible and put on with a swab. Either 
good when the wind blows. Or saponified or red oil used 
with a swab along the seams. Solder flows more freely 
than with rosin alone. 



120 Tables, Rules and Recipes. 

SOLDERING FLUID OR FLUX. 

Prussiate of potash, borax and copperas, each i dram ; 
sal ammoniac Yi ounce, muriatic acid 3^ ounces, well 
mixed, then add as much zinc as it will dissolve. Add 
I pint or more water according to strength required. 

Anq-THer. 
Sal ammoniac and borax, each i dram; chloride of 
^inc I ounce, water i pint. It will not eat copper or tar- 
nish tin. Use less water and it will be stronger. 



THE NEW ^ ^ 
METAL WORKER 
PATTERN BOOK. 

A Treatise on Pattern Cutting as Applied 
to all Branches of Sheet Metal Work. 

By GEORGE W. KITTREDGE. 

430 Pages; 744 Illustrations; ^ize, 10 x 13 
inches, Cloth Bound, Price, ° - $5.00. 

This is the Most Elaborate and Complete Work that has ever 
been brought out for the use of Sheet Metal Pattern Cutters. 

It is printed from new type with a new and improved arrangement, 
especially convenient for reference and study. 

Parts of the former treatise, entitled The Metal Worker Pattern Book, 
have been utilized In the preparation of this 

GREATLY ENLARGED AND IMPROVED WORK, 

but these have been rewritten and simplified, and later methods em- 
bodied which have come into use since the publication of the original work. 

2J8 Problems are now given, 

75 of which are entirely new» e^ «^ 

Apprentices and Students will find the entire subject presented in such 
a manner as will facilitate systematic study. 

Tinners and Cornice Makers will here find elucidated every problem of 
ordinary occurrence, from the simplest to the most complex. 

Triangulation is here lor the first time treated systematically and in a 
way to meet the practical needs of the ti'ade. 

The opening chapters aie devoted to the preliminary information neces- 
sary to give the student a thorough understandintj of the subject, treating 
the topics fully and with appropriate illustrations. The work is comprised 
in the following chapters: 

I. Terms and Definitions— 15 Pages, 
II. Drawing Instruments and Materials— 13 Pages, 

III. Linear Drawing— 6 Pages. 

IV. Geometrical Problems— 35 Pages, 

V. PRINCIPLES OF PATTERN CUTTING-25 Pages, 
VI. PATTERN PROBLEHS (3 Sections)— 325 Pages. 

1. Miter Cuttinff, 

2. Flaring Work, 

3. Tinangulation. 

This work in its perfected form is a complete 

Encyclopedia of Pattern Problems 

for Tinners, Cornice Makers and Sheet Metal Workers. 

DAVID WILLIAMS COMPANY, Publishers, 
232-238 William St., ... - JSfew York, 



Furnace Heating. 

A Practical and Comprehensive Treatise on Warming Buildings 
with Hot Air. By Wii.i,iam G. Snow. With an Appendix 
on Furnace Fittings. 170 pages, 6x9 inches. Cloth 
bound $1.50 

This is the only book that has been brought out which presents 
a systematic and reliable treatment of the warm air furnace 
system of heating. It deals with the various types of furnaces, 
their construction, proper location and setting, together with 
furnace fittings, and all matters pertaining to the installation of 
furnaces and to effective and economical heating by warm air. 
It is recorhmended to practical furnace men, to architects, builders 
and house owners, and to tinners and plumbers in suburban sec- 
tions who do furnace work. 

Partial Summary of Contents by Chapters. 

Chapter I. — Furnaces — Is devoted to Furnace Construction — The 
Relative Proportion of Furnace Parts— Secondary Heating Surface— Econ- 
omy and Efficiency— Heating Capacity and Exposed Wall Surface— Manu- 
facturers' Ratings of Their Own Productions, etc. 

Chapter II.— House Heating— Compares Furnaces and other Appa- 
ratus, and describes Method of Setting Brick and Portable Furnaces- 
Location ami Area of Cold Air Supply— Cold Air Rooms and Air Filters- 
Return Ducts and Air Circulation — Size of Hot Air Pipes— lyocation of 
Registers, etc. 

Chapter III.— The Combination System— Discusses Heating Dis- 
tant Rooms with Radiators— Balancing the vSystem— Location of Water 
Heater in Furnace— Capacity of Water Heaters— Size of Radiators, etc. 

Chapter IV.— Air— Deals with the Necessity of Ventilation— Water 
Needed to Moisten Air— Expansion of Air— Velocity of Air in Tubes, etc. 

Chapter V.— Heating and Ventilation of Buildings— Considers 
the Size of Furnaces Required— Fresh Air Room and Supply— Air Circula- 
tion—Size of Flues— Use of Stack Heaters— Size of Heating Coils in Vent 
Flues, etc. 

Chapter VI.— Heating of Public Buildings, Churches and 
Stores— Is given to the Size of Furnaces Required— Grate Surface in Ven- 
tilated Buildings— Air Supply— Size of Heating and Ventilating Flues- 
Size of Stack Heater, etc. 

Chapter VII.— Fan-Furnace Combination System— Is devoted to 
Positive Warm Currents from Fan Systems— Location of Fan and Driving 
Apparatus— How Good Furnaces are Aided by Fans— Types and Efficiency 
of^Fans— Area of Ducts and Flues, etc. 

Chapter VIII.— Temperature Control. 

Chapter IX.— Estimate and Contract Blanks. 

Chapter X.— Value of Fuels— The Proper Size for Furnace 
Chimneys— with tables. 

APPENDIX. 

Furnace Fittings.— A section of 45 pages dealing with 
the Making of Furnace Casings — Metal Cold Air Boxes — 
Making Furnace Bonnets and Collars — Making Pipe and 
Elbows — Register Boxes and Stack Shoes, etc. 

David Williams Company, Publishers, 
232-238 William Street, New York. 



Kitchen Boiler Connections 

A Selection of Practical Letters and Articles 
Relating to Water Backs and Range Boilers. 

FIFTH EDITION, ENLARGED. 



113 Illustrations ; 195 Pages ; 6x9 in.; Cloth, $1.00 



The Plumbing and Letter Box departments of The Metal 
Worker have contained many articles on the work of setting 
range boilers and overcoming the difficulties commonly encoun. 
tered. The extensive correspondence that the discussion of these 
topics has called forth indicates the widespread interest that they 
attracted, and the letters, coming from all parts of the country 
and from practical men who have written from their personal 
experience, constitute a most valuable source of information. 
The descriptions are plain and the illustrations add all that is 
required to make them clear and comprehensive. 

j These articles have been carefully edited, and are now embod- 
ied in a book, which is divided into two parts, the first on water 
backs and boilers and their connections, and the second on^heat- 
ing rooms from range boilers. 

The main divisions of the volume areas follows : Water Backs 
and Their Construction ; Boiler Construction, Operation, and 
Connections; Circulating Pipes; Multiple Connections; Double 
Boilers; Difficulties Met in Every-day Practice; Rehef Pipe and 
Vacuum Valve; Horizontal Boilers; Miscellaneous; Lime Deposits 
in Water Backs and Boilers; Heating Room from Kitchen Boiler; 
Radiators Heated from Coils in Stoves. 



DAVID WILLIAMS COMPANY, Publishers, 

232-238 WILLIAM STREET, NEW YORK. 



Steam and Hot=Water 
Fitters' Text=Book. 

Prepared for the Steam and Hot-Water Heating 
Course at the New York Trade School, with 
Supplementary Chapters on House Heating, 
Specifications and Surface Estimating. 

BY 

THOMAS Eo McNeill. 



140 pages. Numerous illustrations and diagrams. 5x7 inches. 
Cloth, $1.00. 



This handbook gives in a compact and practical form a series 
of questions and answers, with important supplementary chap- 
ters, covering the subject of steam and hot-water heating in a 
simple way. The need for a text-book of this kind has been 
much felt, and it is believed that this handy manual meets the 
requirement so fully that it will be appreciated by all who wish 
to master the principles, or acquire information in these impor- 
tant systems of heating. 

Beginning with first principles, it progresses in a thorough 
manner, explaining the various systems of steam and hot-water 
heating, as well as the appliances and apparatus used, and the 
manner of connecting them. 



CONTENTS. 



Chap. 



Tools, Fittings and Pipe. 
General Questions on 

Heating. 
Low Pressure .Steam. 
Two Pipe Steam Heating. 
Single Pipe Low Pressure 

Steam Heating. 

6. Indirect Steam Heating, 

7. Hot- Water Heating. 

8. Single Pipe Main System. 

9. High Pressure Steam Heat- 

ing. 



Chap. 10. High and Low Pressure 
Steam Heating and 
Power Plant. 
" II. Exhaust Steam Heating. 
" 12. Power Fan or Blower 
System of Heating and 
Ventilating. 
" 13. Design, Estimate, Speci- 
fication. 
" 14. Dwelling House Heating. 
A Successful Heating Job. 



15- 



David Williams Company, Publishers, 
232-238 William Street, New York. 



PRACTICAL HINTS ON JOINT 
WIPING, 

FOR BEGINNERS IN PLUMBING. 

SIXTH EDITION, ENLARGED. 



With an Appendix, Giving a Selection of Practical 
Letters and Articles compiled from The Metal Worker. 

66 Pages. 41 Illustrations. Paper, 25 Cents. 



This edition contains, besides the two original articles on 
joint wiping, by experts, a selection of letters and articles on vari- 
ous important phases of the subject. 

These include the following : 

Joint Wiping on Copper Pipe. 

Wipe Joints on Brass and Iron. 

Wiping Joints on Tin Pipe. 

Wipe Joint on Lead and Iron Pipe. 

To Make Tight Joints. 

Froze the Pipe to Wipe a Joint. 

Wiping Joints Without a Furnace. j What Breaks Wiped Joints? 

The Effect of a Jar on a Hot Wiped Joint. | Hard Solder to Resist Ammonia. 



What Caused the Joint to Break ? 
Strength of Joints in Lead Pipe. 
Good Wiping Solder. 
Durability of Coarse Solder. 
Plumbers' Paste. 
Cleaning Solder. 



The first article in the book is written by a practical plumber, 
and is illustrated from photographs representing the hands and 
tools when wiping joints in various positions. The second, by an 
expert joint wiper, is also illustrated from photographs, and will 
prove of great assistance to learners. Ample instructions are given 
on preparing the pipes previous to wiping the joints, with full 
descriptions of all tools and appliances used. The pamphlet, in 
short, gives all the assistance that a description of the work can 
furnish, and is the most practical and complete account of joint 
wiping that is published. 

25 CENTS, POSTPAID. 



DAVID WILLIAMS COMPANY, 

2-32-238 William Street, New York. 



WE DEAL IN BOOKS 



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A PRACTICAL JOURNAL 

For Tinners, Roofers, Cornice "Workers, Plumbers and the 
Heating Trades 



SUBSCRIPTION IN UNITED STATES a year 

AND BRITISH AMERICA, $1.00 

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